Question

Use an angle sum identity to verify the identity .

Answer 1

\[\cos 2\theta =2\cos^2 \theta-1\]

Answer 2

\[\cos(x)=\cos(x+x)=\cos(x)\cos(x)-\sin(x)\sin(x)\]
\[=\cos^2(x)-\sin^2(x)\] now replace \(\sin^2(x)\) by \(1-\cos^2(x)\) to get your result

Answer 3

\[\large \cos 2\theta =\cos (\theta +\theta)\]
\[\large =\cos \theta \cos \theta -\sin \theta \sin \theta\]
\[\large =\cos^2 \theta -\sin^2 \theta\]
Using your trig identities:
\[\cos^2 \theta +\sin^2 \theta =1\]
\[\sin^2 \theta =1-\cos^2 \theta\]
\[\large =\cos^2 \theta -(1-\cos^2 \theta)\]

Answer 4

You can finish that last bit off, but make sure you learn your trig identities, double angles until it's printed in your brain.