Question

Evalute
`sin^2((\pi)/(12))`

A. 1/4
B. 3/4
C.
`(2-\sqrt3)/(4)}`
D.
`(2+√(3))/(4)`

PLEASE HELP ME.

Answer 1

Use the double angle identity:



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


Then
`\cos\frac\pi6=\frac{\sqrt3}2`, so you get



`\sin^2\frac\pi{12}=\frac{2-\sqrt3}4`