Simplify the expression by using a doubleangle formula 1 2

Simplify the expression by using a double-angle formula. 1 - 2 sin^2 16degree

Solution

We know that cos 2A = cos² A – sin² A = (1 – sin² A) – sin² A = 1 2 sin² A. Here, A = 16⁰ . Therefore,              1-2sin² 16⁰ = cos (2*16⁰) = cos 32⁰.