Question

Question #23c4e

Answer 1

`cos15˚` can be written as `cos(60˚ - 45˚)`. We use the difference formula for cosine that states `cos(A - B) = cosAcosB + sinAsinB` to expand.

`cos15˚ = cos60˚cos45˚ + sin60˚sin45˚`

We know, by the special triangles, that `cos60˚ = 1/2`, `cos45˚ = sin45˚ = 1/sqrt(2)` and `sin60˚ = sqrt(3)/2`.

`cos15˚ = (1/2)(1/sqrt(2)) +sqrt(3)/2(1/sqrt(2))`

`cos15˚ = 1/(2sqrt(2)) + sqrt(3)/(2sqrt(2))`

`cos15˚ = (1 + sqrt(3))/(2sqrt(2))`

Hopefully this helps!