If y = x 3x, then y_n = - Vidyadip

MCQ

If $y = \sin x\sin 3x,$ then ${y_n} = $

A
${1 \over 2}\left[ {\cos \left( {2x + n{\pi \over 2}} \right) - \cos \left( {4x + n{\pi \over 2}} \right)} \right]$
✓
${1 \over 2}\left[ {{2^{n\,\,}}\cos \left( {2x + n{\pi \over 2}} \right) - {4^n}\cos \left( {4x + n{\pi \over 2}} \right)} \right]$
C
${1 \over 2}\left[ {{4^n}\cos \left( {4x + n{\pi \over 2}} \right) - {2^n}\cos \left( {2x + n{\pi \over 2}} \right)} \right]$
D
None of these

✓

Answer

Correct option: B.

${1 \over 2}\left[ {{2^{n\,\,}}\cos \left( {2x + n{\pi \over 2}} \right) - {4^n}\cos \left( {4x + n{\pi \over 2}} \right)} \right]$

b
(b) $\sin x\sin 3x = \frac{1}{2}[\cos 2x - \cos 4x]$.

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