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

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

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Answer 1 · 2018-03-09T16:08:14

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 $cos^2theta+sin^2theta=1$ }
= $2cos^2theta-1$ { $color(red)("Hence " proved)$ }

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

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