Question

How do you find the exact values of cos(2pi/5)cos(3pi/5)-sin(2pi/5)sin(3pi/5) using the half angle formula?

Answer 1

`color(red)(cos((2π)/5)cos((3π)/5)-sin((2π)/5)sin((3π)/5) =-1)`

Explanation:

It's easier to use the cosine sum identity.

`cos(A+B)= cosAcosB-sinAsinB`

∴ `cosAcosB-sinAsinB = cos(A+B)`

`cos((2π)/5)cos((3π)/5)-sin((2π)/5)sin((3π)/5) = cos((2π)/5+(3π)/5)= cos((5π)/5)=cosπ`

`cos((2π)/5)cos((3π)/5)-sin((2π)/5)sin((3π)/5) =-1`