Question

How do you use the angle sum or difference identity to find the exact value of `sin((5pi)/12)`?

Answer 1

`sin((5pi)/12)=(1+sqrt3)/(2sqrt2)`

Explanation:

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

and `(5pi)/12=(2pi+3pi)/12=(2pi)/12+(3pi)/12=pi/6+pi/4`

`sin((5pi)/12)=sin(pi/6+pi/4)=sin(pi/6)cos(pi/4)+cos(pi/6)sin(pi/4)`

= `1/2xx1/sqrt2+sqrt3/2xx1/sqrt2`

= `(1+sqrt3)/(2sqrt2)`