Question

How do you use the angle sum or difference identity to find the exact value of `sin(pi/3+pi/4)`?

Answer 1

`(sqrt2/4)(sqrt3 + 1)`

Explanation:

Use trig identity -->
sin ( a + b) = sin a.cos b + sin b.cos a
`sin (pi/3 + pi/4) = sin (pi/3).cos (pi/4) + sin (pi/4).cos (pi/3`
Trig table -->
`sin (pi/3) = sqrt3/2` ----- `cos (pi/4) = sqrt2/2`
`sin (pi/4) = sqrt2/2` ----- `cos (pi/3) = 1/2`
`sin (pi/3 + pi/4) = (sqrt3/2)(sqrt2/2) + (sqrt2)/2(1/2) =`
`= (sqrt2/4)(sqrt3 + 1)`