Please show all work ANSWER using formulas not in progam cod

Please show all work. ANSWER using formulas not in progam code.

3. Find the exact value of cos(15) using an identity.

Solution

cos 15

cos (45-30)

This is of the form cos(A-B)=cos A cos B +sinA sin B

cos(45-30)=cos 45 cos 30 + sin 45 sin 30=(sqrt2/2)(sqrt3/2) + (sqrt2/2)(1/2)

                                                                  = (sqrt6/4) + (sqrt2/4)= (sqrt 6+ sqrt2)/4