let's bear in mind that sin(π/2) = 1 and cos(π/2) = 0.
[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left(x-\frac{\pi }{2} \right)\implies sin(x)cos\left( \frac{\pi }{2} \right)-cos(x)sin\left( \frac{\pi }{2} \right) \\\\\\ sin(x)[0]-cos(x)[1]\implies -cos(x)[/tex]
