Express the product as a sum then find the sum’s exact value. cos11𝜋/12cos𝜋/12

Question

I am so confused on what to do. Pls help.

Answer 1

You should look up tthe identities for product of cosines, product of sines, and product of cos and sin. All involve the sum amd difference of cos and sin.

For this particular problem, cosAcosB = 1/2(cos(A+B)+cos(A-B))

Thus, cos(11π/12)cos(π/12) = 1/2(cos(11π/12+1π/12)+cos(11π/12-1π/12)) =

1/2(cos(π)+cos(5π/6)) = 1/2(-1 -√3/2) = (-2 -√3)/4