List of top Mathematics Questions on Trigonometric Identities asked in TS EAMCET

If \(x=\tan A, y=\tan B, z=\tan C\) and \[ xy+yz+zx=1, \] then evaluate \[ \frac{(1-x^2)(1-y^2)(1-z^2)}{(1+x^2)(1+y^2)(1+z^2)} \]

If \[ (\sin\theta+\cos\theta)^4+(\sin\theta-\cos\theta)^4 = p - q(\sin^4\theta+\cos^4\theta), \] then \(p+q=\)

If \(\alpha,\beta\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), \[ \cos^4\alpha=\frac1{16},\qquad \sin^4\beta=\frac1{16} \] then \[ \cos\alpha+\cos\beta= \]

Evaluate \[ 4\sin\frac{\pi}{6}\sin\frac{2\pi}{6}\sin\frac{3\pi}{6}\sin\frac{4\pi}{6}\sin\frac{5\pi}{6} \]

If \[ x=\sin18^\circ \] and \[ y=\tan22\frac12^\circ \] then \[ 4x(4x+2)= \]