Question

Given that cos[a+b]=cos a*cos b-sin a*sin b and sin[a+b]=sin[a+b]=sin a cos b+cos a sin
b.find the value of cos 75 degree by taking suitable values of a and
b.

Answer 1

you can take the value of a and b as 30and45 after that I think you can find it

Answer 2

let a =30 and  b = 45
thus Cos (75) = Cos (30+45)
Thus applying the formula

Cos (30+45) = Cos 30 * Cos 45 - Sin 30 * Sin 45
                      = root 3/2 * 1/root 2 - 1/2 * 1/root2
                      = (root3-1)/ 2root2
               thus the value of Cos 75 = (root3-1)/2root2