Question

cos^43/2x-sin^43/2x=1/2

Answer 1

$cos^4frac{3x}{2}-sin^4frac{3x}{2}=frac{1}{2}\(cos^2frac{3x}{2}+sin^2frac{3x}{2})(cos^2frac{3x}{2}-sin^2frac{3x}{2})=frac{1}{2}\(1)(cos(2*frac{3x}{2})=frac{1}{2}\cos3x=frac{1}{2}\3x=pm frac{pi}{3}+2pi n\x=pm frac{pi}{9}+frac{2pi n}{3}, ; nin Z.$