Question

Evaluate the expression using an appropriate double angle formula.
cos^2(15) - sin^2(15)

Answer 1

cos^2(15) - sin^2(15) = cos 2*15 = cos 30
= (sqrt3)/2

Answer 2

use of the identtiy cos 2x = cos^2x - sin^2x

Answer 3

How? could you please explain in detail please?

Answer 4

there is an established formula:

cos 2x = cos^2x - sin^2x
which is true for all angles x
the reverse is also true:
cos^2x - sin^2x = cos2x
so if you substitute x = 15 you get
cos^2(15) - sin^2(15) = cos(2*15)
cos(2*15) = cos 30

now you can use a calculator to find the cosine of 30
you get 0.866 which is a valid answer

- i used a special right angled triangle