Trigonometric Identities

If $\cos \left(\theta \right)\mathrm{cosec}\left(23°\right) = 1$, then find the value of $\theta$.

What should come in the place of ($?$) for the given expression?

$9{\sec }^2\left(\theta \right) – 9{\tan }^2\left(\theta \right)=?$

Let  $\mathrm{f}\left(\mathrm{x}\right)={\sin }^6\mathrm{x}+{\cos }^6\mathrm{x}+\mathrm{k}({\sin }^4\mathrm{x}+{\cos }^4\mathrm{x})$  for some real number $\mathrm{k},$ then the value of $\mathrm{k}$ for which $\mathrm{f}\left(\mathrm{x}\right)$ is constant for all values of $\mathrm{x}$ is

If  $\alpha +\beta =\frac{\pi }{2}$ and  $\beta +\gamma =\alpha$ , then  $\tan \alpha$  equals –

The value of the expression  $\sqrt{3}\mathrm{cosec}20°-\sec 20°$ is equal to

$\left(1+\cos \frac{\pi }{8}\right)\left(1+\cos \frac{\mathrm{}3\pi }{8}\right)\left(1+\cos \frac{\mathrm{}5\pi }{8}\right)\left(1+\cos \frac{\mathrm{}7\pi }{8}\right)$ is equal to –

If $\alpha +\beta +\gamma =2\pi$, then

Find value of ${\cos }^2\left(\frac{\mathrm{\pi }}{8}\right)$.

Find the value of $\frac{\cos 22{\displaystyle \frac{1}{2}}°-\sin 22{\displaystyle \frac{1}{2}}°}{\cos 22\frac{1}{2}°+\sin 22\frac{1}{2}°}$

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

If $cosec\theta +\cot \theta =6$, then which one of the following is true?

The least value of $\left(2{\sin }^2\theta +3{\cos }^2\theta \right)$ is 

Find the  expansion of $\mathrm{con}\left(nx\right)$and$\sin \left(nx\right)$using complex numbers

If $f\left(\theta \right)=\frac{1-\mathrm{s}\mathrm{i}\mathrm{n}2\theta +\mathrm{c}\mathrm{o}\mathrm{s}2\theta }{2\mathrm{c}\mathrm{o}\mathrm{s}2\theta }$, then value of $f\left(11°\right)f\left(34°\right)$ equals-

A vertical pole stands at a point $A$ on the boundary of a circular park of radius $a$ and blinds an angle $\alpha$ at another point $B$ on the boundary. If the chord $AB$ subtends an angle $\alpha$ at the centre of the park, then the height of the pole is