Question

cos2θ = cos^2θ − 1/2

Answer 1

is this proving \[\cos2\theta=\cos^{2}\theta - \frac{1}{2}\]
\[\cos2\theta = \cos(\theta+\theta)=\cos \theta \cos \theta - \sin \theta \sin \theta = \cos^{2}\theta-\sin^{2}\theta\]
\[\cos2\theta = \cos^{2}\theta-(1-\cos^{2}\theta)=2\cos^{2}\theta-1\]
dividing right-hand side by 2, proves that
\[\cos2\theta = \cos^{2}\theta-\frac{1}{2}\]

Answer 2

Trigonometric Identities used are as follows:
\[\cos(\alpha+\beta)=\cos \alpha \cos \beta - \sin \alpha \sin \beta\]
\[\sin^{2}\alpha+\cos^{2}\alpha=1\]
and \[\cos2\alpha = 2 \cos^{2}\alpha -1\]