Prove the identity with steps.
Remember that a double angle formula for cosine is\(\cos(2x)=\cos^{2}x-\sin^{2}x\)So\(\cos^{2}(2x)-\sin^{2}(2x)=\cos(4x)\)\(\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos(2*2x)\)\(\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos^{2}(2x)-\sin^{2}(2x)\)
