Simplify without a calculator: 1−2sin^2(15°)

Question

Simplify without a calculator: 1 - 2sin²(15°)

Answer 1

one version of the general formula for double angle of cosine is

cos2x = 1-2sin^2x

if x =15 then

cos30 = 1-2sin^2(15)

cos30 = sqr3/2

that's from a right triangle with sides 1- sqr3 - 2

adjacent side (sqr3) over hypotenuse (2) gives sqr3/2= cos30