Question

How do you find the exact value of `cos(pi/4+pi/3)`?

Answer 1

`cos(pi/4+pi/3) = (sqrt2-sqrt6)/4`

Explanation:

In order to evaluate `cos(pi/4+pi/3)` we need to use the compound angle formula for cos: `cos(A+B) -= cosAcosB-sinAsinB`

`therefore cos(pi/4+pi/3) = cos(pi/4)cos(pi/3)-sin(pi/4)sin(pi/3) = 1/sqrt2 *1/2 - 1/sqrt2*sqrt3/2 = 1/(2sqrt2)-sqrt3/(2sqrt2) = (1-sqrt3)/(2sqrt2)=(sqrt2-sqrt6)/4`