Introduction to Trigonometric Functions

If$2\sin x\sin y+3\cos y+6\cos x\sin y=7$
Then find $2{\tan }^{2}x+{\tan }^{2}y =?$

If $\theta =\frac{17\mathrm{\pi }}{3}$ then $\tan \theta -cot\theta =$

What is the maximum value of $3\left(\sin x-\cos x\right)+4\left({\cos }^{3}x-{\sin }^{3}x\right) ?$

Find the value of of $sec\left(270°-\theta \right)sec\left(90°-\theta \right)-\tan \left(270°-\theta \right)\tan \left(90°+\theta \right)$

The equation ${\sin }^{2}x=\frac{a^2+b^2}{2ab}$ is possible if

If $A=\sin \left[co{t}^{-1}\left\{\cos \left({\tan }^{-1}x\right)\right\}\right]$, then 

$\sin \theta +\cos \theta =\frac{\sqrt{7}}{2}$ then the value of ${\sin }^6\theta +{\cos }^6\theta +6{\sin }^2\theta {\cos }^2\theta$ is equal to

Find the value of $\cos \left(-1710°\right)$.

In $△ABC$, if $BC$ is unity , $\sin \frac{A}{2}=x_1, \sin \frac{B}{2}=x_2, \cos \frac{A}{2}=x_3$ and $\cos \frac{B}{2}=x_4$ with ${\left(\frac{x_1}{x_2}\right)}^{2021}-{\left(\frac{x_3}{x_4}\right)}^{2020}=0$ then the length of $AC$ is 

Prove that $2(\cos ec 4A+cot 4A)=cot A-\tan A$

The integer just greater than the least value of $f\left(x\right)=3{\sin }^{2}x+5\sin x+7$ is

Value of $\sin 1080=?$

Prove that ${\sin }^{4}A-{\cos }^{4}A=2{\sin }^{2}A-1$

If $\tan \theta =\frac{3}{4}$ and $\theta$ is not in $1^{st}$ Quadrant, then find the value of $\frac{\sin \left(90+\mathrm{\theta }\right)-\cot \left(180-\mathrm{\theta }\right)}{\tan \left(270-\mathrm{\theta }\right)-\cos \left(270+\mathrm{\theta }\right)}$.

Find the value of $\sin \left(\frac{20\mathrm{\pi }}{3}\right)$

If $\sin \theta +\cos \theta =0$ and $\theta$ lies in the $4th$ quadrant, find $\sin \theta$ and $\cos \theta$. 

The value of ${\sin }^{2}51°+{\sin }^{2}39°$ is 

Is ${\sin }^{2}x$ and ${\left(\sin x\right)}^2$ same$?$

If $\tan x=\frac{3}{4}, \pi <x<\frac{3\pi }{2}$, find the value of $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$.

If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.