Amit M Agarwal Solutions for Chapter: Trigonometric Functions and Equations, Exercise 6: Entrances Gallery

The value of $\frac{\sin {55}^{°}-\cos {55}^{°}}{\sin {10}^{°}}$ is

If $\alpha ,\beta \in \left[0,\frac{\pi }{2}\right], \sin \alpha =\frac{4}{5}$ and $\cos \left(\alpha +\beta \right)=-\frac{12}{13}$, then $\sin \beta$ is equal to

If $\tan \alpha =\frac{b}{a},a>b>0$ and $0<\alpha <\frac{\pi }{4},$ then $\sqrt{\frac{a+b}{a-b}}-\sqrt{\frac{a-b}{a+b}}$ is equal to 

The value of $\frac{\cot x-\tan x}{\cot 2x}$ is

The number of points of intersection of $2y=1$ and $y=\sin x$ in $-2\pi \le x\le 2\pi$ is

The value of $x$ in $\left(0,\frac{\pi }{2}\right)$  satisfying the equation $\sin x\cos x=\frac{1}{4}$ is

The number of solutions of $\cos 2\theta =\sin \theta$ in $\left(0,2\pi \right)$ is

If $\sin 6\theta +\sin 4\theta +\sin 2\theta =0$, then the general values of $\theta$ are