Question

Trig question -- please help if you can!

Answer 1

$\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ y=r[cos(\theta +R)]\implies y=r[cos(\theta )cos(R)-sin(\theta )sin(R)] \\\\\\ y=rcos(\theta )cos(R)-rsin(\theta )sin(R) \\\\\\ z=r[sin(\theta +R)]\implies y=r[sin(\theta )cos(R)+cos(\theta )sin(R)] \\\\\\ z=rsin(\theta )cos(R)+rcos(\theta )sin(R)$