Question

prove that cos2 theta = cos square theta ‐ sin square theta​

Answer 1

Answer:

Step-by-step explanation:

To Prove :-

$\sf cos2\theta=cos^2\theta-sin^2\theta$

Solution :-

Taking L.H.S :-

$\sf = cos2\theta$

$= cos(\theta+\theta)$

We know that :-

cos(A + B) = cosAcosB - sinAsinB

$= cos\theta\times cos\theta - sin\theta\times sin\theta$

$= cos^2\theta-sin^2\theta$

= R.H.S

Know More :-

Taking :-

$= cos^2\theta-sin^2\theta$

$= 1 - sin^2\theta-sin^2\theta$

$= 1 - 2sin^2\theta$

$= 1 - 2(1 - cos^2\theta)$

$= 1 - 2 +2cos^2\theta$

$= 2cos^2\theta-1$

Hence we can write :-

$1) cos2\theta = 1 - 2 sin^2\theta$

$2) cos2\theta=2cos^2\theta-1$

Answer 2

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