Question

How do you find the exact value of the expression `sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)`?

Answer 1

`sqrt3/2`

Explanation:

`sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)`

we use

`sin(alpha+beta)=sinalphacosbeta+sinbetacosalpha`

comparing this with the question we have

`sin(pi/12+pi/4)`

`=sin((4pi)/12)=sin(pi/3)=sqrt3/2`