Question

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

Answer 1

`sin(pi/6)cos(pi/2)+cos(pi/6)sin(pi/2)=sqrt3/2`

Explanation:

As `sinAcosB+cosAsinB=sin(A+B)`

substituting `A=pi/6` and `B=pi/2`, we get

`sin(pi/6)cos(pi/2)+cos(pi/6)sin(pi/2)`

= `sin(pi/6+pi/2)`

= `cos(pi/6)` - as `sin(pi/2+x)=cosx`

= `sqrt3/2`