## Trigonometry (11th Edition) Clone

$$\cos^215^\circ-\sin^215^\circ=\frac{\sqrt3}{2}$$
$$X=\cos^215^\circ-\sin^215^\circ$$ - 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, $$\cos^215^\circ-\sin^215^\circ=\frac{\sqrt3}{2}$$