Question

Verify that sin (π + q) = -sin q is an identity.

Answer 1

Bearing in mind that cos(π) is -1, and sin(π) is 0, then

$\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\ -------------------------------\\\\ sin(\pi +q)=sin(\pi )cos(q)+cos(\pi )sin(q) \\\\\\ sin(\pi +q)=0\cdot cos(q)+(-1)\cdot sin(q)\implies sin(\pi +q)=-sin(q)$