Question

how to find the exact value of: cos(9*pi/12)*cos(5*pi/12)+sin(9*pi/12)*sin(5*pi/12)

Answer 1

9pi/12 should be converted into degrees. The value of pi is 180 so all you do is 180 times 9 divided by 12 and then take the cosine of that value.

Answer 2

cosx cosy + sinx siny = cos(x-y)

so, what we have here is

cos(9π/12 - 5π/12) = cos(4π/12) = cos π/3 = 1/2