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

Question

Accepted Answer

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

Answer

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

Answer

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

Answer

None of these

differentiation