Question

Which sum or difference identity could be used to prove that sin(π + q) = -sin q

is an identity?

Answer 1

sinπcosq + cosπsinq

Explanation:

This was the answer on edg

i'm just as clueless so I'm trying to help from my mistakes

Answer 2

we should know that :

sin ( a + b ) = sin a * cos b + sin b cos a

For the given equation :

sin (π + q) = sin π * cos q + sin q * cos π

sin π = zero and cos π = -1

∴ sin (π + q) = 0 * cos q + sin q * (-1) = - sin q

Another solution:

The angle (π + q) lies in the third quarter ⇒ (1)

(π + q) and (-q) are supplementary angles ⇒ (2)

From (1) and (2)

sin(π + q) = -sin q