If \(\cos x=-\frac{1}{2}\) and \(\pi , find the value of \(4\tan^2x-3cosec^2x\)

Evaluate \(\cot\left(\frac{-15\pi}{4}\right)\)

In any quadrilateral ABCD, prove that sin (A + B) + sin (C + D) = 0

Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)