Amit M Agarwal Solutions for Chapter: Trigonometric Equations and Inequations, Exercise 3: Objective Questions

The general solution of the equation, $\frac{1-\sin x+\cdots +(-1{)}^n{\sin }^{n}x+\cdots }{1+\sin x+\cdots +{\sin }^{n}x+\cdots }=\frac{1-\cos 2x}{1+\cos 2x}$ is 

The number of solutions of the equation, ${\sin }^{5}x-{\cos }^{5}x=\frac{1}{\cos x}-\frac{1}{\sin x}\left(\sin x\ne \cos x\right)$ is :

$\mathrm{}$$6{\tan }^{2}x-2{\cos }^{2}x=\cos 2x$ (where $x\ne \frac{\mathrm{\pi }}{2}$) if:

$\tan \left(\frac{p\mathrm{\pi }}{4}\right)=\cot \left(\frac{q\pi }{4}\right)$ if

If $\sin x=\cos y, \sqrt{6}\sin y=\tan z$ and $2\sin z=\sqrt{3}\cos x; u, v, w$ denotes respectively ${\sin }^{2}x,{\sin }^{2}y,{\sin }^{2}z$, then the value of the triplet $\left(u,v,w\right)$ is

$\cos 2x-3\cos x+1=$ $\frac{1}{\left(\cot 2x-\cot x\right)\sin \left(x-\pi \right)}$ holds if : 

The value '$a$' for which the equation $4{cosec}^2\left(\pi \left(a+x\right)\right)+a^2-4a=0$ has a real solution is:

Total number of solutions of $\sin x.\tan 4x=\cos x$ belonging to $\left(0,\pi \right)$ are