Answer
$$\cos^215^\circ-\sin^215^\circ=\frac{\sqrt3}{2}$$
Work Step by Step
$$X=\cos^215^\circ-\sin^215^\circ$$
- From Double-Angle Identity for cosine: $$\cos2A=\cos^2A-\sin^2A$$
So if you replace the above identity with $A=15^\circ$ as in $X$, we get
$$X=\cos(2\times15^\circ)$$
$$X=\cos30^\circ$$
$$X=\frac{\sqrt3}{2}$$
Therefore, $$\cos^215^\circ-\sin^215^\circ=\frac{\sqrt3}{2}$$
