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If $fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 tan space theta cot space theta equals negative 1$ ,then

$θ \in (0, \frac{π}{2})$
$θ \in (0, \frac{π}{2})$
$θ \in (π, \frac{3 π}{2})$
$θ \in (\frac{3 π}{2}, 2 π)$

hint Hint:

we have given trigonometry function. Which is
$fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 tan space theta cot space theta equals negative 1$
We have to find where θ is belongs. Solve the function and find the answer.

The correct answer is: $theta element of open parentheses fraction numerator 3 pi over denominator 2 end fraction comma 2 pi close parentheses$

Here, We have to find where θ is belongs.
Firstly, we have given
$fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 tan space theta cot space theta equals negative 1$ ---(1)
$fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 equals negative 1$ [since, $fraction numerator tan space theta space equals space 1 over denominator c o t space theta end fraction$ ]
We know that,
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis left parenthesis a squared plus a b plus b squared right parenthesis$
$1 plus fraction numerator sin theta cos theta minus cos theta over denominator open parentheses square root of left parenthesis 1 plus 2 cos squared theta – 1 end root close parentheses end fraction – 2 equals negative 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket c o t 2 theta equals 2 c o s squared theta – 1 right square bracket 1 plus fraction numerator sin theta cos theta minus cos theta over denominator open parentheses square root of 2 left parenthesis cos squared theta end root close parentheses end fraction – 2 equals negative 1 1 plus s i n theta c o s theta minus fraction numerator cos theta over denominator square root of 2 c o s theta – 2 end root end fraction equals negative 1 1 plus s i n theta c o s theta – fraction numerator 1 over denominator square root of 2 – 2 end root end fraction equals negative 1 s i n theta c o s theta – fraction numerator 1 over denominator square root of 2 end fraction equals 0 s i n theta c o s theta equals fraction numerator 1 over denominator square root of 2 end fraction$
For every θ for sin and cos is $straight pi over 4$ . so for But θ not possible in second quadrant because cos is negative,
Then θ always belongs to ( 0 , $straight pi over 2$ ).
Therefore the correct answer is θ ∈ ( 0 , $straight pi over 2$ ).
$fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 tan space theta cot space theta equals negative 1$

In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = $fraction numerator 1 over denominator square root of 2 end fraction$ so θ always lies between ( 0 , $straight pi over 2$ ) .

If $6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals$

maths-General

General

maths-

The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

maths-General

General

maths-

The general solution of the equation, $2 cot space theta over 2 equals left parenthesis 1 plus co t space theta right parenthesis squared$ is

maths-General

General

Maths-

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

Maths-General

In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.

General

maths-

Let S = $open curly brackets x element of left parenthesis negative pi comma pi right parenthesis colon x not equal to 0 comma plus-or-minus pi over 2 close curly brackets$ The sun of all distinct solution of the equation $square root of 3 sec space x plus cosec space x plus 2 left parenthesis tan space x minus cot space x right parenthesis equals 0$

maths-General

General

physics-

A wave motion has the function $y equals a subscript 0 end subscript sin invisible function application left parenthesis omega t minus k x right parenthesis.$ The graph in figure shows how the displacement $y$ at a fixed point varies with time $t.$ Which one of the labelled points shows a displacement equal to that at the position $x equals fraction numerator pi over denominator 2 k end fraction$ at time $t equals 0$

physics-General

General

maths-

For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

maths-General

General

Chemistry

Which of the following pairs of compounds are functional isomers?

ChemistryGeneral

General

Maths-

Let $theta comma ϕ element of left square bracket 0 comma 2 pi right square bracket$ be such that $2 cos space theta left parenthesis 1 minus sin space ϕ right parenthesis equals sin squared space theta open parentheses tan space theta over 2 plus co t space space theta over 2 close parentheses cos space ϕ minus 1 comma tan space left parenthesis 2 pi minus theta right parenthesis greater than 0$ and $negative 1 less than sin space theta less than negative fraction numerator square root of 3 over denominator 2 end fraction$ Then $ϕ$ cannot satisfy

In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = $fraction numerator 2 over denominator sin x end fraction$ .

Let $theta comma ϕ element of left square bracket 0 comma 2 pi right square bracket$ be such that $2 cos space theta left parenthesis 1 minus sin space ϕ right parenthesis equals sin squared space theta open parentheses tan space theta over 2 plus co t space space theta over 2 close parentheses cos space ϕ minus 1 comma tan space left parenthesis 2 pi minus theta right parenthesis greater than 0$ and $negative 1 less than sin space theta less than negative fraction numerator square root of 3 over denominator 2 end fraction$ Then $ϕ$ cannot satisfy

Maths-General

General

maths-

The number of all possible values of $theta$ , where 0< $theta$ < $straight pi$ , which the system of equations $left parenthesis straight y plus straight z right parenthesis cos space 3 theta equals xyzsin space 3 theta xsin space 3 theta equals fraction numerator 2 cos space 3 theta over denominator straight y end fraction plus fraction numerator 2 sin space 3 theta over denominator straight z end fraction$ $x y z sin space 3 theta equals left parenthesis y plus 2 z right parenthesis cos space 3 theta plus y sin space 3 theta$ has a solution $open parentheses straight x subscript 0 comma straight y subscript 0 comma straight z subscript 0 close parentheses$ with $straight y subscript straight c comma straight z subscript 0 not equal to 0$ , is

maths-General

General

maths-

Roots of the equation $2 sin squared space theta plus sin squared space theta equals 2$ are

maths-General

General

Chemistry

Isomers are possible for the molecular formula

ChemistryGeneral

General

Maths-

The number of solutions of the pair of equations $2 sin squared space theta minus cos space 2 theta equals 0 comma 2 cos squared space theta minus 3 sin space theta equals 0$ in the interval [0, 2 $straight pi$ ] is

Maths-General

General

chemistry-

Quantitative estimation of $Fe to the power of 2 plus end exponent$ can be made by $KMnO subscript 4$ in acidified medium. In which medium it can be estimated by $KMnO subscript 4 space$ ?

chemistry-General

General

maths-

If $fraction numerator sin to the power of 4 invisible function application A over denominator a end fraction plus fraction numerator cos to the power of 4 invisible function application A over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction$ then the value of $fraction numerator sin to the power of 8 end exponent invisible function application A over denominator a to the power of 3 end exponent end fraction plus fraction numerator cos to the power of 8 end exponent invisible function application A over denominator b to the power of 3 end exponent end fraction$ is equal to

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$θ \in (0, \frac{π}{2})$
$θ \in (0, \frac{π}{2})$
$θ \in (π, \frac{3 π}{2})$
$θ \in (\frac{3 π}{2}, 2 π)$

The correct answer is: $theta element of open parentheses fraction numerator 3 pi over denominator 2 end fraction comma 2 pi close parentheses$

Related Questions to study

If $6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals$

If $6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals$

The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

The general solution of the equation, $2 cot space theta over 2 equals left parenthesis 1 plus co t space theta right parenthesis squared$ is

The general solution of the equation, $2 cot space theta over 2 equals left parenthesis 1 plus co t space theta right parenthesis squared$ is

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

Which of the following pairs of compounds are functional isomers?

Which of the following pairs of compounds are functional isomers?

Roots of the equation $2 sin squared space theta plus sin squared space theta equals 2$ are

Roots of the equation $2 sin squared space theta plus sin squared space theta equals 2$ are

Isomers are possible for the molecular formula

Isomers are possible for the molecular formula

The number of solutions of the pair of equations $2 sin squared space theta minus cos space 2 theta equals 0 comma 2 cos squared space theta minus 3 sin space theta equals 0$ in the interval [0, 2 $straight pi$ ] is

The number of solutions of the pair of equations $2 sin squared space theta minus cos space 2 theta equals 0 comma 2 cos squared space theta minus 3 sin space theta equals 0$ in the interval [0, 2 $straight pi$ ] is

Quantitative estimation of $Fe to the power of 2 plus end exponent$ can be made by $KMnO subscript 4$ in acidified medium. In which medium it can be estimated by $KMnO subscript 4 space$ ?

Quantitative estimation of $Fe to the power of 2 plus end exponent$ can be made by $KMnO subscript 4$ in acidified medium. In which medium it can be estimated by $KMnO subscript 4 space$ ?

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If ,then

we have given trigonometry function. Which isWe have to find where θ is belongs. Solve the function and find the answer.

The correct answer is:

Here, We have to find where θ is belongs.Firstly, we have given ---(1) [since, ]We know that, For every θ for sin and cos is . so for But θ not possible in second quadrant because cos is negative,Then θ always belongs to ( 0 , ).Therefore the correct answer is θ ∈ ( 0 , ).

Related Questions to study

If

If

The most general solution of the equations is

The most general solution of the equations is

The general solution of the equation, is

The general solution of the equation, is

The most general solution of cot = and cosec = – 2 is :

The most general solution of cot = and cosec = – 2 is :

Let S = The sun of all distinct solution of the equation

Let S = The sun of all distinct solution of the equation

A wave motion has the function The graph in figure shows how the displacement at a fixed point varies with time Which one of the labelled points shows a displacement equal to that at the position at time

A wave motion has the function The graph in figure shows how the displacement at a fixed point varies with time Which one of the labelled points shows a displacement equal to that at the position at time

For , the equation has

For , the equation has

Which of the following pairs of compounds are functional isomers?

Which of the following pairs of compounds are functional isomers?

Let be such that and Then cannot satisfy

Let be such that and Then cannot satisfy

The number of all possible values of , where 0< < , which the system of equations has a solution with , is

The number of all possible values of , where 0< < , which the system of equations has a solution with , is

Roots of the equation are

Roots of the equation are

Isomers are possible for the molecular formula

Isomers are possible for the molecular formula

The number of solutions of the pair of equations in the interval [0, 2] is

The number of solutions of the pair of equations in the interval [0, 2] is

Quantitative estimation of can be made by in acidified medium. In which medium it can be estimated by ?

Quantitative estimation of can be made by in acidified medium. In which medium it can be estimated by ?

If then the value of is equal to

If then the value of is equal to

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The correct answer is: $theta element of open parentheses fraction numerator 3 pi over denominator 2 end fraction comma 2 pi close parentheses$

If $6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals$

If $6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals$

The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

The general solution of the equation, $2 cot space theta over 2 equals left parenthesis 1 plus co t space theta right parenthesis squared$ is

The general solution of the equation, $2 cot space theta over 2 equals left parenthesis 1 plus co t space theta right parenthesis squared$ is

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

The most general solution of cot $theta$ = $square root of 3$ and cosec $theta$ = – 2 is :

For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

Roots of the equation $2 sin squared space theta plus sin squared space theta equals 2$ are

Roots of the equation $2 sin squared space theta plus sin squared space theta equals 2$ are

The number of solutions of the pair of equations $2 sin squared space theta minus cos space 2 theta equals 0 comma 2 cos squared space theta minus 3 sin space theta equals 0$ in the interval [0, 2 $straight pi$ ] is

The number of solutions of the pair of equations $2 sin squared space theta minus cos space 2 theta equals 0 comma 2 cos squared space theta minus 3 sin space theta equals 0$ in the interval [0, 2 $straight pi$ ] is

Quantitative estimation of $Fe to the power of 2 plus end exponent$ can be made by $KMnO subscript 4$ in acidified medium. In which medium it can be estimated by $KMnO subscript 4 space$ ?

Quantitative estimation of $Fe to the power of 2 plus end exponent$ can be made by $KMnO subscript 4$ in acidified medium. In which medium it can be estimated by $KMnO subscript 4 space$ ?