$\tan 5x - \tan 3x - \tan 2x$ is equal to

The value of the expression $2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta) + 1$ is

Given the equation $4x^2 + 4(a - 1)x + (1 - 2a) = 0$ has roots $\sin \theta$ and $\cos \theta$ where $0 < \theta < \frac{\pi}{2}$,then the maximum value of $(a + \sin \theta)$ is:

If the roots of the quadratic equation $x^2 + px + q = 0$ are $\tan 30^\circ$ and $\tan 15^\circ$ respectively,then the value of $2 + q - p$ is

$\Delta XYZ$ is right-angled at $Y$. If $m \angle X = 60^{\circ}$,then find the value of $\left(\sec Z + \frac{2}{\sqrt{3}}\right)$.

If $\tan A = n \tan B$ and $\sin A = m \sin B ,$ then the value of $\cos ^{2} A$ is