Question

How do you prove `sin(pi/6 + x) + sin (pi/6 - x)= cosx`?

Answer 1

`sin (pi/6 + x) = sin (pi/6).cos x + sin x.cos (pi/6)` (1)
`sin (pi/6 - x) = sin (pi/6).cos x - sin x.cos (pi/6)` (2).

Add up (1) and (2) -->
`Sum = 2sin (pi/6).cos x`.
Trig table gives --> `sin (pi/6) = 1/2`
Therefor,
`S = 2(1/2)cos x = cos x.`