Question

How do you use the angle sum or difference identity to find the exact value of `sin(pi/2-pi/6)`?

Answer 1

`sqrt3/2`.

Explanation:

We will use `: sin(A-B)=sinAcosB-cosAsinB`

Also, `sin(pi/2)=1, cos(pi/2)=0, sin(pi/6)=1/2, &, cos(pi/6)=sqrt3/2`.

Hence, `sin(pi/2-pi/6)=1*sqrt3/2-0*1/2=sqrt3/2`.