Trigonometric Functions and Properties

Find the least value of $(4{\sec }^2\theta +9{\mathrm{cosec}}^2\theta )$.

If $0\le \theta \le 2\mathrm{\pi }$, solve the equation:

$4\tan \left(\theta \right)+2=2\tan \left(\theta \right)$

The maximum value of $1+\sin \left(\frac{\mathrm{\pi }}{4}+\theta \right)+2\cos \left(\frac{\mathrm{\pi }}{4}-\theta \right), \theta \in R$ equals

If $2{\cos }^2\mathrm{\theta }-5\mathrm{cos\theta }+2=0$,  $0°<\mathrm{\theta }<90°$, then the value of $(\mathrm{sec\theta }+\mathrm{tan\theta })$ is

If $\cos \left(2\mathrm{\theta }+54°\right)=\mathrm{sin\theta }$, $0°<\left(2\mathrm{\theta }+54°\right)<90°$, then what is the value of $\frac{1}{\cot 5\theta +\sec \frac{5\theta }{2}}?$

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

Find the value of $\frac{\left(3\sin \left({\displaystyle \frac{3\mathrm{\pi }}{2}-a}\right)-4{\sin }^3\left({\displaystyle \frac{3\mathrm{\pi }}{2}-a}\right)\right)}{\left(3\cos \left(\frac{3\mathrm{\pi }}{2}-a\right)-4{\cos }^3\left(\frac{3\mathrm{\pi }}{2}-a\right)\right)}$ :

What should come in the place of $\left(?\right)$ of the expression given below?

$-\frac{\sin \left(\frac{3\pi }{2}+x\right)}{2\cos \left(\frac{3\pi \hspace{0.17em}}{2}+x\right)}+\frac{\cos \left(\frac{3\pi \hspace{0.17em}}{2}+x\right)}{2\sin \left(\frac{3\pi \hspace{0.17em}\hspace{0.17em}}{2}+x\right)}=?$

What should come in the place of $\left(?\right)$ for the expression given below?

$\frac{{\tan }^3\left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)-3\tan \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}{1-3{\tan }^2\left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}=?$

What should come in the place of $\left(?\right)$ for the expression given below?

$\frac{1+\sin \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}{\cos \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}-\frac{1-\sin \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}{\cos \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}-\frac{2}{\tan \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)}=?$

What should come in the place of $\left(?\right)$ of the expression given below?

$\frac{\left(3\sin \left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)-4{\sin }^3\left({\displaystyle \frac{3\mathrm{\pi }}{2}}+x\right)\right)}{\left(3\cos \left(\frac{3\mathrm{\pi }}{2}+x\right)-4{\cos }^3\left(\frac{3\mathrm{\pi }}{2}+x\right)\right)}=?$

Find the value of the trigonometric function at the given angles.

$y=\sin \left(\frac{7\mathrm{\pi }}{6}\right)\sec \left(\frac{\mathrm{\pi }}{3}\right)+{\left(\sin \left(\frac{11\mathrm{\pi }}{6}\right)\sec \left(\frac{\mathrm{\pi }}{3}\right)\right)}^7$

Find the value of the trigonometric function at the given angles.

$y=\sin \left(\frac{5\mathrm{\pi }}{3}\right)\sin \left(\frac{\mathrm{\pi }}{3}\right)+{\left(\cos \left(\frac{7\mathrm{\pi }}{4}\right)\right)}^4+\sin \left(\frac{\mathrm{\pi }}{6}\right)$

Find the value of :

$Sin 75°+Sin 105°+Sin 90°+Sin 0°$

Solve the equation :

$\frac{Cos \varnothing }{1-\tan \varnothing }+\frac{Sin \varnothing }{1-Cot \varnothing }$

If $600$ revolutions are made by an iron Wheel in $2$ minutes. Then, through how many radians will it turn in one second?

If $960$ revolutions are made by a wheel in $2$ minutes. Then through how many radians it will turn in one second?

Find the value of ;

$Sin 105°+Cos105°-Cos45°$

If Coso $=\frac{4}{5}$and Sin$= \frac{7}{8}$ , Where$\varnothing$and $\varnothing$both lies in the first quadrant , Find the value of : $Sin \left(\theta +\varnothing \right)$ .

Find the value of :

$Sin 105°+Cos105°+Sin105°$$+ Cos 105° + Sin 45°$