Question

cosA cos2A cos4A cos8A=sin16A/16sinA

Answer 1

You can use the result here:

https://brainly.com/question/11990269

This identity suggests that

$\cos A\cos2A\cos4A\cos8A=\dfrac{\cos A+\cos3A+\cos5A+\cdots+\cos15A}8$

From here, you can use the sum/difference identities for cosine.

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

$\implies\cos x\cos y=\dfrac{\cos(x+y)+\cos(x-y)}2$

Apply these carefully to the right hand side and it should reduce quite nicely to the same expression on the left.