Prove the identity by changing the left side of the equation to show equivalency to the right side. Please show all steps.

cos^4ø - sin^4ø = 1 - 2sin^2ø

Question

Prove the identity by changing the left side of the equation to show equivalency to the right side. Please show all steps.

cos^4ø - sin^4ø = 1 - 2sin^2ø

mathmale · Answer

Hint:  the left side of this equation is a "difference of two squares."  Rewrite (cos 4*theta)^4 - (sin 4*theta)^4 as [(cos 4*theta)^2]^2 + [(cos 4*theta)^2]^2.  Factor this by treating it as the difference of two squares.  What do you think the next step should be?

anonymous · Answer

I could think to factor it into (cos2(4x)+sin2(4x))(cos2(4x)−sin2(4x))
Am I on the right track?