Amit M Agarwal Solutions for Chapter: Trigonometric Functions and Equations, Exercise 3: Work Book exercise 9.3

If the equation $\left(\cos p-1\right)x^2+\left(\cos p\right)x+\sin p=0$, where $x$ is a variable, has real roots, then, all values of $p$ lies in the set $A$. Then a subset of $A$ is

The smallest positive root of the equation $\tan x-x=0,$ lies in 

General solution of the equation $\left(\sqrt{3}-1\right)\sin \theta +\left(\sqrt{3}+1\right)\cos \theta =2$ is

In a right-angled triangle, the hypotenuse is $2\sqrt{2}$ times the length of perpendicular drawn from the opposite vertex on the hypotenuse, then the other two angles are

The solution set of $\left(2\cos x-1\right)\left(3+2\cos x\right)=0$ in the interval $0\le x\le 2\pi ,$ is

The most general value of $\theta$ which satisfies both the equations $\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}},$ will be

General solution of $4\cot 2\theta ={\cot }^2\theta -{\tan }^2\theta$ is

If the expression $\frac{\sin \frac{x}{2}+\cos \frac{x}{2}-i\tan x}{1+2i\sin \frac{x}{2}}$ is real, then $x$ is equal to