Question

Verify the identity. sin quantity x plus pi divided by two = cos x

Answer 1

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