Question

How do you use the double angle or half angle formulas to prove `sin(pi+x) = - sinx`?

Answer 1

Prove sin (pi + x) = - sin x

Explanation:

Apply the trig identity: sin (a + b) = sin a.cos b + sin b.cos a
`sin (pi + x) = sin pi.cos x + sin x.cos pi.`
Since `sin pi = 0` and `cos pi = -1`, therefor,

`sin (pi + x) = - sin x`