Question

If cos x = −6/7, and 90° < x < 180°, what is cos⁡(2x)?

Answer 1

Recall the double angle identity:

$\cos2x=\cos^2x-\sin^2x=2\cos^2x-1$

Then

$\cos2x=2\left(-\dfrac67\right)^2-1=\dfrac{23}{49}$