bearing in mind that cos(π) is -1, and sin(π) is 0, then
[tex]\bf \textit{Sum and Difference Identities}
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sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\
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sin(\pi +q)=sin(\pi )cos(q)+cos(\pi )sin(q)
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sin(\pi +q)=0\cdot cos(q)+(-1)\cdot sin(q)\implies sin(\pi +q)=-sin(q)[/tex]
