Question

Simplifique: sen( x - 60°) + cos(x + 60°)

Answer 1

sen60=√3/2
cos60=1/2........

Answer 2

$\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)$

$\sin(x-60)=\\ \sin(x)\cos(60)-\sin(60)\cos(x) \\\frac{\sin(x)}{2}-\frac{\cos(x)\sqrt{3}}{2}$

$\cos(x+60)=\\ \cos(x).\cos(60)-\sin(x).\sin(60) \\ \frac{\cos(x)}{2}-\frac{\sqrt{3}\sin(x)}{2}$

$\sin(x-60)+\cos(x-60)= \\ \frac{\sin(x)}{2}-\frac{\cos(x)\sqrt{3}}{2}+\frac{\cos(x)}{2}-\frac{\sqrt{3}\sin(x)}{2}$

$(\sin(x)+\cos(x))(\frac{1-\sqrt{3}}{2})$