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 $\tan \theta =-\frac{4}{3},$ then $\sin \theta$ is –

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

If $y\left(x\right)=\sin x$, the minimum value of $\sin x$ is 

If $\tan A+\cot A=5$, then ${\tan }^{4}A+{\cot }^{4}A$ is equal to

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 $\tan \left(315°\right)$.

If $\theta$ be an acute angle and $\sec \theta =\frac{13}{5}$, then what is the value of perpendicular?

If $\theta$ be an acute angle and $\sec \theta =\frac{13}{5}$ then in which quadrant does $\sec (180°+\mathrm{\theta })$ lie?

If $\theta$ be  an acute angle and $\sec \theta =\frac{13}{5}$, then the value of $\cot (270°-\theta )$ is?

If $\theta$ be acute angle and $\sec \theta =\frac{13}{5}$ then the value of $\sin (90°-\theta )$ is?