Question

How do you find the value of `sin15` using the double or half angle formula?

Answer 1

sin 15=`(sqrt3 -1)/(2sqrt2)`

Explanation:

Use the identity `cos 2theta= 1- 2sin^2 theta`and put `theta`= 15.

Thus `cos 30= 1-2sin^2 15`

`sqrt3 /2= 1-2sin^2 15`

`sin^2 15=1/2 (1-sqrt3 /2)` =`(2-sqrt3)/4= (4-2sqrt3)/8 = (sqrt3 -1)^2 /8`

sin 15=`(sqrt3 -1)/(2sqrt2)`