Question

Can you prove that ? cos2θ = 2cos^2θ-1 ......thanks

Answer 1

see below

Explanation:

We have,`cos2theta=cos(theta+theta)`
Or,applying `cos(a+b)=cosacosb-sinasinb`,we see,
`cos2theta=costheta xxcostheta-sinthetaxxsintheta`
=`cos^2theta-(1-cos^2theta)` {since `cos^2theta+sin^2theta=1`}
=`2cos^2theta-1` {`color(red)("Hence " proved)`}