Question

Find the value of $\frac{\sin 5\theta }{\sin \theta }$.

• A. $(16{\cos }^4\theta -12{\cos }^2\theta +1)$
• B. $(16{\cos }^4\theta +12{\cos }^2\theta +1)$
• C. $(16{\cot }^4\theta -12{\cos }^2\theta -1)$
• D. $(16{\cos }^4\theta +12{\cos }^2\theta -1)$

Answer 1

The correct option is A $(16{\cos }^4\theta -12{\cos }^2\theta +1)$

Given

$\frac{\sin 5\theta }{\sin \theta }$

Let $\theta =\frac{\pi }{3}$

$⟹\frac{\sin \frac{5\pi }{3}}{\sin \frac{\pi }{3}}$

$⟹\frac{\sin (2\pi -\frac{\pi }{3})}{\sin \frac{\pi }{3}}$

$⟹\frac{-\sin \frac{\pi }{3}}{\sin \frac{\pi }{3}}$

$⟹-1$

option A

$⟹16{\cos }^4\theta -12{\cos }^2\theta +1$

$⟹16{\cos }^4\frac{\pi }{3}-12{\cos }^2\frac{\pi }{3}+1$

$⟹16\frac{1}{2^4}-12\frac{1}{2^2}+1$

$⟹1-3+1=-1$

Hence A is correct answer