If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

The value of the $\sin 1^{\circ} + \sin 2^{\circ} + \ldots + \sin 359^{\circ}$ is equal to

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x + 2 b \sin x = c$,$x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ has two distinct real roots $\alpha$ and $\beta$ with $\alpha + \beta = \frac{\pi}{3}$. Then the value of $\frac{b}{a}$ is

${\left( \frac{\cos A + \cos B}{\sin A - \sin B} \right)^n} + {\left( \frac{\sin A + \sin B}{\cos A - \cos B} \right)^n}$ (where $n$ is an integer) $=$

If $\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)$,then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=$

If $\operatorname{Sinh}^{-1} x = \log 3$ and $\operatorname{Cosh}^{-1} y = \log \frac{3}{2}$,then $\operatorname{Tanh}^{-1}(x-y) = $