Basics of Trigonometry

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

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

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

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 $x$?

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 _____.

A, B, C are three points on a circle. The tan gent at A meets BC produced at T,∠ BTA = 38⁰,∠ CAT = 42⁰. The angle subtended by BC at the centre of the circle is-

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

If $\tan \left(\theta \right)·\cos (60°)=\frac{\sqrt{3}}{2}$, then what should come in the place of ($?$) for the expression given below?

$\sin (\theta -15°)=?$

From the top of a light-house at a height $20$ $\mathrm{m}$ above sea-level, the angle of depression of a ship is $30°$. The distance of the ship from the foot of the light-house is _____.

Find the value of the following expression:

$\sin \left(1°\right)\sin \left(2°\right)\sin \left(3°\right)...............\sin \left(196°\right)$

In a right-angled triangle ABC, $\sin (A+B) = 1$ and $\cos A =\frac{1}{2}$ . Find the value of $\cos (C – B)$?

Find the value of $\frac{{\tan }^{2}30°}{se{c}^{2}30°}+\frac{\cos e{c}^{2}45°}{co{t}^{2}45°}-\frac{se{c}^{2}60°}{\cos e{c}^{2}60°}$.

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

${\sin }^2\left(60°\right){\cos }^2\left(45°\right)+2{\tan }^2\left(60°\right)-{\mathrm{cosec}}^2\left(30°\right)=?$

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

$\frac{\tan \left(13°\right)\tan \left(36°\right)\tan \left(45°\right)\tan \left(54°\right)\tan \left(77°\right)}{2{\sec }^2\left(60°\right)\left({\sin }^{2}60°-3\cos 60°+2\right)}=?$

Find the value of ${\sec }^4\left(\theta \right)\left(1-{\sin }^4\left(\mathrm{\theta }\right)\right)-2{\tan }^2\left(\mathrm{\theta }\right)$.

The value of $\frac{se{c}^{2}60°{\cos }^{2}45°+\cos e{c}^{2}30°}{cot30°se{c}^{2}45°-\cos e{c}^{2}30°\tan 45°}$ is:

Find the value of ${\sin }^{2}60°+{\cos }^{2}30°-{\sin }^{2}45°-3{\sin }^{2}90°$.

If $\sin \left(20+x\right)°=\cos \left(60°\right), 0\le \left(20+x\right)\le 90$, then find the value of $2{\sin }^2\left(3x+15\right)°-{\mathrm{cosec}}^2\left(2\mathrm{x}+10\right)°$.

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

$\tan \left(35°\right)·\cot \left(40°\right)·\tan \left(45°\right)·\cot \left(50°\right)·\tan \left(55°\right)=?$