## Trigonometry (11th Edition) Clone

$$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$ 1 is matched with C.
$$X=2\cos^215^\circ-1$$ Recall the double-angle identities: $$2\cos^2A-1=\cos2A$$ Here $X$ is like the form of $2\cos^2A-1$ with $A=15^\circ$. Therefore, $$X=2\cos^215^\circ-1=\cos(2\times15^\circ)$$ $$X=\cos30^\circ$$ $$X=\frac{\sqrt3}{2}$$ So, $$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$ We pick C here.