If cos2A = 1-2sin^2A prove that sin15 = √2-√3/2?
1 Answer
Apr 16, 2018
If we let
#cos(2(15˚)) = 1- 2sin^2(15˚)#
It follows that
#cos(30˚) = 1 -2sin^2(15˚)#
#sqrt(3)/2 = 1 - 2sin^2(15˚)#
#2sin^2(15˚) = 1 - sqrt(3)/2#
#sin^2(15˚) = (2 - sqrt(3))/4#
#sin(15˚) = sqrt((2 - sqrt(3))/4)#
#sin(15˚) = sqrt(2 -sqrt(3))/2#
As required.
Hopefully this helps!
