Trigonometric Ratios

The expression $\sqrt{2+\sqrt{2+\sqrt{2+2 \cos \left(8\theta \right)}}}$ is equal to what?

If $2\cos \left(\theta \right)-\sin \left(\theta \right)=\frac{1}{\sqrt{2}}$ and $\left(0°<\theta <90°\right)$, then the value of $2\sin \left(\theta \right)+\cos \left(\theta \right)$ is:

If $\mathrm{tan\theta }=\frac{\mathrm{x} \sin \mathrm{a}}{1-\mathrm{x} \cos \mathrm{a}}$  and  $\tan \mathrm{a}=\frac{\mathrm{y} \mathrm{sin\theta }}{1-\mathrm{y} \mathrm{cos\theta }}$, then $\frac{\mathrm{x}}{\mathrm{y}}$ equals to ______.

If sin17⁰ $$=\frac { x }{ y }$$, then sec 17⁰ - sin 73⁰ is equal to

If $\alpha +\beta =90°$ and $\alpha :\beta =2:1$, then what is the ratio of $\tan \left(\alpha \right):\tan \left(\beta \right)$?

The angles of depression of Two ships from the top of a lighthouse are $45°$ and $30°$ towards east, if the ships are $200 \mathrm{m}$ apart, the height of lighthouse is$?$ (Take $\sqrt{3}= 1.73$ )

How much time does the minute hand of a watch take to describe an angle of $\frac{3\mathrm{\pi }}{2}$ radians ?

What is the value of $\left(\sin 43° \cos 47°+\cos 43° \sin 47°\right)$?

Find the value of ${sin}^{2}A+\left[\left(\frac{1}{1+{tan}^{2}A}\right)\right]$:

If $\tan \left(\frac{\mathrm{\pi }}{2}-\frac{\theta }{2}\right)=\sqrt{3}$, then value of $\cos \left(\theta \right)$ is:

If $\frac{\sin \left(x+y\right)}{\sin \left(x-y\right)}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{a}-\mathrm{b}}$ , then the value of $\frac{\tan x}{\tan y}$ is equal to_____.

If $\sin \left(\mathrm{x}-\mathrm{y}\right)=\frac{1}{2}$ and $\cos \left(\mathrm{x}+\mathrm{y}\right)=\frac{1}{2}$ , then what is the value of $x$?

The value of $\sin 18º + \cos 36º?$

A kite is flying at a height of $50$ $\mathrm{m}$. If the length of string is $100$ $\mathrm{m}$ then the inclination of string to the horizontal ground in degree measure is _____.

Which is not correct?

If $\tan \theta +\cot \theta =2$, then what is $\sin \theta +\cos \theta$ equal to?

If $\mathrm{sin\theta }+\mathrm{cosec\theta }=2$, then what is the value of ${\sin }^2\mathrm{\theta }+{\mathrm{cosec}}^5\mathrm{\theta }$ when $0°\le \theta \le 90°$?

If $x\sin \left(60°\right)\times \tan \left(30°\right)=\sec \left(60°\right)\times \cot \left(45°\right)$, then find the value of $x$.

If $\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=3$ then the value of ${\sin }^4\theta -{\cos }^4\theta$is ?

If ${\tan }^{2}45°-{\cos }^{2}60°=x\sin 45°·\cos 45°·\tan 60°$, then find the value of $x$.