Prove that:`\ (sin3A+sin A)sin A+(cos3A-cos A)cos A=0`

Explanation

Given `(sin 3 A+sin A) sin A+(cos 3 A-cos A) cdot cos A`



`(sin 3 A+sin A) sin A+(cos 3 A-cos A) cdot cos A
{[ sin A+sin B=2 sin (frac{A+B}{2}) cdot cos (frac{A-B}{2}).}
cos A-cos B=-2 sin (frac{A+B}{2}) cdot sin (frac{A-B}{2}.`



`sin A+sin B=2 sin (frac{A+B}{2}) cdot cos (frac{A-B}{2})
.cos A-cos B=-2 sin (frac{A+B}{2}) cdot sin (frac{A-B}{2})]`


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