Trigonometric Functions and Properties

Suppose $f\left(x\right)=\tan \left({\sin }^{-1}\left(2x\right)\right)$. Find range of $f\left(x\right)$.

${\sec }^2\theta =\frac{4xy}{{(x+y)}^2}$ is true if and only if

Given  $A={\sin }^2\theta +{\cos }^4\theta$ , then for all real values of  $\theta$

Let  $\theta \in \left(0,\frac{\pi }{4}\right)$  and  $t_1={\left(\tan \theta \right)}^{\tan \theta },t_2={\left(\tan \theta \right)}^{\cot \theta },t_3={\left(\cot \theta \right)}^{\tan \theta }\mathrm{and}{t}_4={\left(\cot \theta \right)}^{\cot \theta }$ , then –

Given both $\theta$ and  $\varphi$  are acute angles  $\sin \theta =\frac{1}{2}, \cos \varphi =\frac{1}{3}$, then the value of  $(\theta +\varphi )$ belongs to 

If  $\alpha +\beta +\gamma =\mathrm{}\mathrm{}\mathrm{}2\pi ,\mathrm{then}$ –

If $\theta$ is acute and $\sin \theta =\cos 2\theta$, then $(\sin \theta +\cos \theta )=?$

Find the range of $f\left(x\right)={cosec}^{2}x+25{\sec }^{2}x$.

Find the value of $\sec \left(315°\right)$.

Find the value of $\cos \left(315°\right)$.

Find the value of $\sin \left(315°\right)$.

Find the value of $\cot \left(315°\right)$.

Find the value of $\tan \left(315°\right)$.

The maximum value of $1+\sin \left(\frac{\mathrm{\pi }}{6}+\theta \right)+2\cos \left(\frac{\mathrm{\pi }}{3}-\theta \right)$ for real values of $\theta$ is

What is the value of $\tan \frac{7\mathrm{\pi }}{6}$?

Number of solutions of the equation $\sin x=\frac{x}{4\pi }$ is :

If in a triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ sines of angles $\mathrm{A}$ and $\mathrm{B}$ satisfy the equation $4\mathrm{ }{\mathrm{x}}^{\mathrm{ }2\mathrm{ }}-\mathrm{ }2\sqrt{6}\mathrm{x}+1\mathrm{ }=\mathrm{ }0$ , then $\cos \left(\mathrm{A}\mathrm{ }-\mathrm{ }\mathrm{B}\right)$ is equal to -

The minimum value of $|\sin B|+|\cos B|$ is -