Question

Use the sum-to-product identities to rewrite the following expression as a product.sin(x) – sin(3x)

Answer 1

Given:

$\sin x-\sin 3x$

Sol:.

Formula of sin3A is:

$\sin 3A=3\sin A-4\sin ^3A$

Put the value of sin3x in given function:

$\begin{gathered} =\sin x-\sin 3x \\ =\sin x-(3\sin x-4\sin ^3x) \\ =\sin x-3\sin x+4\sin ^3x \\ =-2\sin x+4\sin ^3x \\ =2\sin x(2\sin ^2x-1) \end{gathered}$