Basics of Trigonometry

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-

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

If $\tan \theta =-\frac{4}{3},$ then $\sin \theta$ is –

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

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

If $\cos h\left(2x\right)=199,$ then $\cot hx=$

The value of $\sin \frac{31\pi }{3}$ is

If a flagstaff of $6 \mathrm{metres}$ high placed on the top of a tower throws a shadow of $2\sqrt{3} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}$ along the ground, then find the angle (in degrees) that the sun makes with the ground.

$\cos 1°·\cos 2°·\cos 3°·\dots .·\cos 179°=$

If $x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3},$ then ($xy + yz + zx$) is equal to

Let $n$ be a positive integer such that $\sin \frac{\pi }{2n}+\cos \frac{\pi }{2n}=\frac{\sqrt{n}}{2},$ then

What is the value of $\frac{(\sin {30}^{°}+ \cos {30}^{°})}{(\cos {30}^{°}- \sin {30}^{°})}$?

Which of the following statement is correct?

If $\tan 17°=x$, then show that $\frac{\tan 163°-\tan 107°}{1+\tan 163°·\tan 107°}=\frac{1-x^2}{2x}$.

If $3 \sin \theta +4 \cos \theta =5$, then show that $\sin \theta =\frac{3}{5}$,

If $\tan \theta +\sin \theta =m, \tan \theta -\sin \theta =n$ then prove that $mn={\tan }^2\theta .{\sin }^2\theta$ and $4\sqrt{mn}=m^2-n^2, \left(m>n\right)$

Prove that ${\cos }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}=2$.

Find the value of $\cos 1° \cos 2° \cos 3° \dots \cos 179°$.

If ${\tan }^2\theta =2{\tan }^2\varphi +1$, then find $\cos 2\theta +{\sin }^2\varphi$

If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$, then find the value of $\cos \theta -\sin \theta$.