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!