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 _____.

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 _____.

Which of the following is the pair of adjacent angles in the given figure.

If $?? + ??= 90°$, then the value of ${\sec }^2?? - {\cot }^2??$ is _____.

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

If $0°<\theta <90°$ and $(\sin \theta +cosec\theta )=\frac{5}{2}$, then $\theta =?$

Value of $\cos 1°·\cos 2°·\cos 3°\dots ..\cos 180°=$

If $\cot \theta =-3/4$, then $\sin \theta =$

If ${\sin }^2\theta =\frac{1}{4}$ and $0<\theta <90°$, then the value of $\tan \theta$ is equal to

Two parallel chords are drawn on the same side of the centre of a circle of radius $20.$ It is found that they subtend $60°$ and $120°$ angles at the centre of the circle, then the perpendicular distance between the chords is

Find $x$ if $2 {\sin }^{2}x-1=0$.

In a triangle $ABC$, the altitude $AD$ and the median $AE$ divide $\angle A$ into three equal parts. If $BC=28$, then the nearest integer to $AB+AC$ is

Find the value of $cosec750°-2\left(\cot 765°\right)$