Question

How do you use the angle sum identity to find the exact value of `sin105`?

Answer 1

see below

Explanation:

`sin 105^@=sin(60^@+45^@)`-> use formula `sin(A+B)=sinAcosB+cosAsinB`

`sin(60^@+45^@)=sin60^@cos45^@+cos60^@sin45^@`

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

`=sqrt6/4+sqrt2/4`

`=(sqrt6+sqrt2)/4`