Maths-
General
Easy

Question

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

  1. Infinitely many solutions
  2. Three solutions
  3. One solutions
  4. No solutions

The correct answer is: One solutions

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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

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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.

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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

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

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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

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Isomers are possible for the molecular formula

Isomers are possible for the molecular formula

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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, 2straight pi] is

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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 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

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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If 0 less than theta less than 2 pi, then the intervals of values of theta for which 2 sin squared space theta minus 5 sin space theta plus 2 greater than 0, is

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. X is an unsaturated gaseous hydrocarbon. Find X?

. X is an unsaturated gaseous hydrocarbon. Find X?

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The eq. wt. of Na subscript 2 straight S subscript 2 straight O subscript 3 in the reaction, Na subscript 2 straight S subscript 2 straight O subscript 3 plus 5 straight H subscript 2 straight O plus 4 Cl subscript 2 not stretchy rightwards arrow 2 NaHSO subscript 4 plus 8 HClis/are:

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Which statement(s) is/are wrong?

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To solve a trigonometric inequation of the type sin x ≥ a where |a| ≤ 1, we take a hill of length 2straight pi  in the sine curve and write the solution within that hill. For the general solution, we add 2nstraight pi. For instance, to solve sin space x greater or equal than negative 1 half, we take the hill open square brackets negative pi over 2 comma fraction numerator 3 pi over denominator 2 end fraction close square brackets over which solution is negative pi over 6 less than X less than fraction numerator 7 pi over denominator 6 end fraction The general solution is 2 straight n pi minus pi over 6 less than straight x less than 2 straight n pi plus fraction numerator 7 pi over denominator 6 end fraction, n is any integer. Again to solve an inequation of the type sin x ≤ a, where |a| ≤ 1, we take a hollow of length 2straight pi in the sine curve. (since on a hill, sinx ≤ a is satisfied over two intervals). Similarly cos x ≥ a or cosx ≤a, |a| ≤ 1 are solved.

Solution to the inequation sin to the power of 6 space x plus cos to the power of 6 space x less than 7 over 16 must be

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Solution to the inequation sin to the power of 6 space x plus cos to the power of 6 space x less than 7 over 16 must be

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Which of the following compounds does not give halo form reaction?

Which of the following compounds does not give halo form reaction?

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The oxidation number of carboxylic carbon atom in CH subscript 3 COOH is:

The oxidation number of carboxylic carbon atom in CH subscript 3 COOH is:

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