Question

How do you simplify `sin (π/3 + a)`?

Answer 1

`1/2(sqrt(3)cosalpha+sinalpha)`

Explanation:

We have, `color(red)(sin(A+B)=sinAcosB+cosAsinB)`
Taking, `A=pi/3and B=alpha`, we get
`sin(pi/3+alpha)=sin(pi/3)cosalpha+cos(pi/3)sinalpha` `=sqrt(3)/2cosalpha+1/2sinalpha=1/2(sqrt(3)cosalpha+sinalpha)`