How do you show that cos?

How do you show that cos 2θ = 1 – 2 sin^2 θ?

Answer:
See explanation…

Explanation:
Given that:

\(\cos 2 \theta=\cos ^{2} \theta-\sin ^{2} \theta\)

and,

\(\cos ^{2} \theta+\sin ^{2} \theta=1\)

we find,

\(\cos 2 \theta=\left(1-\sin ^{2} \theta\right)-\sin ^{2} \theta=1-2 \sin ^{2} \theta\)