[tex]\bf sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
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\textit{also recall that }cos\left( \frac{\pi }{2} \right)=0\qquad \qquad sin\left( \frac{\pi }{2} \right)=1\\\\
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sin\left( x+\frac{\pi }{2} \right)\implies sin(x)cos\left( \frac{\pi }{2} \right)+cos(x)sin\left( \frac{\pi }{2} \right)
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sin(x)\cdot 0+cos(x)\cdot 1\implies \boxed{cos(x)}[/tex]
