Question

Evalute i}{12}) " alt=" sin^2(\frac{\pi}{12}) " align="absmiddle" class="latex-formula">
A. 1/4
B. 3/4
C. $\frac{2-\sqrt3}{4}}$
D. $\frac{2+\sqrt{3}}{4}$

PLEASE HELP ME.

Answer 1

Use the double angle identity:


$\sin^2\dfrac\pi{12}=\dfrac{1-\cos\frac\pi6}2$


Then $\cos\dfrac\pi6=\dfrac{\sqrt3}2$, so you get


$\sin^2\dfrac\pi{12}=\dfrac{2-\sqrt3}4$