I have worked out how to do it, just I need to know how to solve it without calculator.

Find the exact value of:

2 cos²15 - 1

this is what i did:

2 cos²15 - 1so

= cos²15 + sin²15 = 1side note:sin²15 = 1 - cos²15hence:2 cos²15 - 1

then i did:

2 cos²15 - 1would initially be:cos²15 + sin²15

= cos(15 + 15)

= cos 15 x cos 15 - sin 15 x sin 15

= root 3 / 2

What i wanna know is, i could not of done this without a calculator...

What is the alternative method?

(sorry if i made this very confusing)