How do you verify the identity $cos^4theta-sin^4theta=cos^2theta-sin^2theta$ ?

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Answer 1 · 2016-09-18T14:35:40

Factor the left hand side as a difference of squares:

$(cos^2theta + sin^2theta)(cos^2theta - sin^2theta) = cos^2theta - sin^2theta$

Apply the pythagorean identity $cos^2theta + sin^2theta = 1$ :

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

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

$LHS = RHS$

Hopefully this helps!

How do you verify the identity cos^4theta-sin^4theta=cos^2theta-sin^2thetacos^4theta-sin^4theta=cos^2theta-sin^2theta?