Amit M Agarwal Solutions for Chapter: Trigonometric Functions and Identities, Exercise 3: Objective Questions

If $\tan x-{\tan }^{2}x=1$, then the value of ${\tan }^{4}x-2{\tan }^{3}x-{\tan }^{2}x+2\tan x+1$ is

The minimum value of $3{\tan }^2\theta +12{\cot }^2\theta$ is

For any real $\theta$, the maximum value of ${\cos }^2\left(\cos \theta \right)+{\sin }^2\left(\sin \theta \right)$ is 
 

If $\sqrt{1-\sin A}=\sin \frac{A}{2}-\cos \frac{A}{2},$ then $\frac{A}{2}-\frac{\pi }{4}$ could lie in quadrant

If $\sin x+\cos x=\sqrt{y+\frac{1}{y}}, x\in [0,\pi ]$, then

If $x=\sec \varphi -\tan \varphi$ and $y=cosec\varphi +\cot \varphi ,$ then

In an isosceles right-angled triangle, a straight line drawn from the midpoint of one of the equal sides to the opposite angle. It divides the angle into two parts, $\theta$ and $\left(\frac{\pi }{4}-\theta \right).$ Then tan $\theta$ and $\tan \left(\frac{\pi }{4}-\theta \right)$ are equal to
 

If $3{\sin }^{2}A+2{\sin }^{2}B=1$ and $3\sin 2A-2\sin 2B=0,$ where $A$ and $B$ are acute angles, then $\left(A+2B\right)$ is equal to