Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The sum of the series, $sin space theta sec space 3 theta plus sin space 3 theta sec space 3 squared theta plus sin space 3 squared theta sec space 3 cubed theta plus times times$ upto n terms, is

$\frac{1}{2} [\tan 3^{n} θ - \tan 3^{x - 1} θ]$
$[\tan 3^{n} θ - \tan θ]$
$\frac{1}{2} [\tan 3^{n} θ - \tan θ]$
$\frac{1}{2} (\tan 3^{n} θ - 1)$

hint Hint:

In the question we will simplify each term using trigonometric identities separately and then try to find any pattern in the series, then we will add the terms to get the sum of the series.

The correct answer is: $1 half open square brackets tan space 3 to the power of n theta minus tan space theta close square brackets$

Sn= $sin space theta sec space 3 theta plus sin space 3 theta sec space 3 squared theta plus sin space 3 squared theta sec space 3 cubed theta plus times times$ upto n terms.
$N o w comma space sin theta. s e c 3 theta equals fraction numerator sin theta over denominator cos 3 theta end fraction 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 space space space equals fraction numerator 2 sin theta. cos theta over denominator 2 cos 3 theta. cos theta end fraction 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 space space space equals 1 half. fraction numerator sin 2 theta over denominator cos theta cos 3 theta end fraction 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 space space space equals 1 half open parentheses fraction numerator sin open parentheses 3 theta minus theta close parentheses over denominator cos theta. cos 3 theta end fraction close parentheses 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 space space space equals 1 half open parentheses fraction numerator sin 3 theta cos theta minus cos 3 theta sin theta over denominator cos theta. cos 3 theta end fraction close parentheses 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 space space space equals 1 half open parentheses fraction numerator sin 3 theta over denominator cos theta end fraction minus fraction numerator sin theta over denominator cos theta end fraction close parentheses 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 space space space equals 1 half open parentheses tan 3 theta minus tan theta close parentheses S i m i l a r l y comma space sin 3 theta. s e c 9 theta equals 1 half open parentheses tan 9 theta minus tan theta close parentheses comma space sin 9 theta. s e c 27 theta equals 1 half open parentheses tan 27 theta minus tan 9 theta close parentheses comma space sin 3 to the power of open parentheses n minus 1 close parentheses end exponent theta. s e c 3 to the power of n theta equals 1 half open parentheses tan 3 to the power of n theta minus tan 3 to the power of open parentheses n minus 1 close parentheses end exponent theta close parentheses S o comma space S n equals 1 half open parentheses tan 3 theta minus tan theta close parentheses plus 1 half open parentheses tan 9 theta minus tan theta close parentheses plus 1 half open parentheses tan 27 theta minus tan 9 theta close parentheses plus..... plus 1 half open parentheses tan 3 to the power of n theta minus tan 3 to the power of open parentheses n minus 1 close parentheses end exponent theta close parentheses space space space space equals 1 half open parentheses tan 3 theta minus tan theta plus tan 9 theta minus tan theta plus tan 27 theta minus tan 9 theta plus...... plus tan 3 to the power of n theta minus tan 3 to the power of open parentheses n minus 1 close parentheses end exponent theta close parentheses space space space space equals 1 half open parentheses tan 3 to the power of n theta minus tan theta close parentheses space space space space space space space space space space space space$

Related Questions to study

In a triangle $ABC$

In a triangle $ABC$

The value of $sum from n equals 1 to straight infinity of fraction numerator tan begin display style space end style open parentheses theta over 2 to the power of n close parentheses over denominator 2 to the power of n minus 1 end exponent cos space theta over 2 to the power of n minus 1 end exponent end fraction$ is

The value of $sum from n equals 1 to straight infinity of fraction numerator tan begin display style space end style open parentheses theta over 2 to the power of n close parentheses over denominator 2 to the power of n minus 1 end exponent cos space theta over 2 to the power of n minus 1 end exponent end fraction$ is

If the equation $cot to the power of 4 space x minus 2 cos space e c squared x plus a squared$ =0 has at least one solution, then the sum of all possible integral values of 'a' is equal to

If the equation $cot to the power of 4 space x minus 2 cos space e c squared x plus a squared$ =0 has at least one solution, then the sum of all possible integral values of 'a' is equal to

parallel

$cos to the power of 6 space pi over 16 plus cos to the power of 6 space fraction numerator 3 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 5 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 7 pi over denominator 16 end fraction$ =

$cos to the power of 6 space pi over 16 plus cos to the power of 6 space fraction numerator 3 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 5 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 7 pi over denominator 16 end fraction$ =

If $a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals$ d then the minimum value of $vertical line cos space theta vertical line$ is equal to (where is variable)

If $a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals$ d then the minimum value of $vertical line cos space theta vertical line$ is equal to (where is variable)

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

parallel

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

parallel

If $tan space theta minus cot space theta equals a$ and $cos space theta minus sin space theta equals b$ then $open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared$

If $tan space theta minus cot space theta equals a$ and $cos space theta minus sin space theta equals b$ then $open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared$

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

parallel

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

physics-General

The value of $cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction$

The value of $cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.