Question

What is the best first step if your plan is to find the exact value of cos 75°using the cosine angle sum identity?

Answer 1

Cos 75  = cos (45 + 30)  = cos45 cos30 - sin45 sin30

=   1/ sqrt2 * sqrt3/2  - 1/ sqrt2 *  1/2

= sqrt3 / 2 sqrt2 - 1 / 2 sqrt2

=     sqrt3 - 1
     -------------
       2 sqrt2