Exact values cot sec cosec

Question

If $\cot(x) = -12/5$ where $x$ is in $[\pi/2,\pi]$, find $\cos(x +\pi/3)$. What trig identity should you use? And how to bring it back to $\cos(x +\pi/3)$?

Answer 1

$Hint :$ Use formula of $cos(x+\frac {\pi} 3)$. Use $\csc(x) ^2 - \cot(x) ^2 = 1$ and $\sin(x)^2 + \cos(x)^2 = 1 $. Don't forget to put appropriate sign to $\cos(x)$ as you will find value of its square.