How to prove $sin^2 theta - cos^2 theta = 1 -2cos^2 theta$ ?

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Answer 1 · 2018-07-17T03:04:41

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Given: Prove $sin^2 theta - cos^2 theta = 1 - 2 cos^2 theta$

Use the Pythagorean Identity: $" "sin^2 theta+ cos^2 theta = 1$

Rearrange the identity: $" "sin^2 theta = 1 - cos^2 theta$

Start with the left side of the equation and substitute the rearranged identity:

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

Combine like-terms:

$= 1 - 2 cos^2 theta$ This is the right-side

Q.E.D.

How to prove sin^2 theta - cos^2 theta = 1 -2cos^2 thetasin^2 theta - cos^2 theta = 1 -2cos^2 theta ?