Question

How do you express `cos(pi/ 4 ) * sin( ( 13 pi) / 12 )` without using products of trigonometric functions?

Answer 1

It can be evaluated as follows

Explanation:

`cos(pi/4)sin(13pi/12)`
`=cos(pi/4)sin(pi+pi/12)`
`=-cos(pi/4)sin(pi/12)`
`=-cos(pi/4)sqrt(1/2(1-cos(pi/6)`
`=-1/sqrt(2)sqrt(1/2(1-sqrt3/2)`
`=-1/sqrt(2)sqrt(1/8(4-2sqrt3)`
`=-1/sqrt(2)sqrt(1/8(sqrt3-1)^2`
`=-(sqrt3-1)/4`
is it OK ?