If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta + 15 \sin \theta = 15$,then $15 \cos \theta - 8 \sin \theta = $

Let $a, b, c$ be the sides of a triangle. If $t$ denotes the expression $\frac{a^2+b^2+c^2}{ab+bc+ca}$,the set of all possible values of $t$ is

If $\theta \in \left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$, then the value of $\sqrt{4 \cos^{4} \theta + \sin^{2} 2 \theta} + 4 \cot \theta \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

$\sin \frac{2 \pi}{5}+\sin \frac{4 \pi}{5}+\sin \frac{6 \pi}{5}+\sin \frac{8 \pi}{5}$ is equal to

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to