Question

verify that the following equation is an identity.
(sin 36 x=4 sin 9 x cos 9 x cos 18 x)
to verify the identity, start with the more complicated side and transform it to look like the other side. choose the correct transformation and transform the expression at each step.
(4 sin 9 x cos 9 x cos 18 x)
= (cos 18 x)

Explanation:

Step1: Use double - angle identity

The double - angle identity for sine is \(\sin(2\alpha)=2\sin\alpha\cos\alpha\). Let \(\alpha = 3x\), then \(\sin(6x)=\sin(2\times3x)\).
By the double - angle identity \(\sin(6x)=2\sin(3x)\cos(3x)\)

Answer:

\(2\sin(3x)\cos(3x)\)