In a triangle $ABC$,if $a^2-b^2-c^2=bc(\lambda^2-2\lambda-1)$,then

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$. Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to

In $\triangle ABC$,we are given that $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$. Then,the measure of $\angle C$ is $....^{\circ}$

If triangle $ABC$ is right-angled at $A$ and $\tan \frac{B}{2}, \tan \frac{C}{2}$ are roots of the equation $ax^2 + bx + c = 0$ $(a \neq 0)$,then:

The sides of a triangle inscribed in a given circle subtend angles $\alpha, \beta, \gamma$ at the center. The minimum value of the $A.M.$ of $\cos (\alpha + \frac{\pi}{2})$,$\cos (\beta + \frac{\pi}{2})$ and $\cos (\gamma + \frac{\pi}{2})$ is equal to

The general value of $\theta$ that satisfies both the equations $\cot^3\theta + 3\sqrt{3} = 0$ and $\csc^5\theta + 32 = 0$ is $(n \in I)$.