# Recent questions tagged trigonometry

1

If $\{ (2 \sin \theta – \cos \theta) / (\cos \theta + \sin \theta) \} = 1,$ then the value of $\tan \theta$ is :$\frac{1}{3}$$\frac{1}{2}$$2$$3$

2

If $\sin 3A = \cos (A – 26^{\circ}),$ where $3A$ is an acute angle then the value of $A$ is :$29^{\circ}$$31^{\circ}$$39^{\circ}$$23^{\circ}$

3

If $\sec \theta + \tan \theta = \sqrt{3},$ then the positive value of $\sin \theta$ is :$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$\frac{1}{\sqrt{3}}$$\sqrt{3}$

4

If $ \ Sinx+Sin^{2} x=1$ then $ \ Cos^{8}x+ 2 \ Cos^{6} x+ \ Cos^{4} x$ equals to :$0$$-1$$1$$2$

5

$ \sin^{-1}\left [ \frac{3}{5} \right ] + \tan^{-1}\left [ \frac{1}{7} \right ]=$$\frac{\pi }{4}$$\frac{\pi }{2}$$ \cos^ {-1} \frac{4}{5} $$\pi$

6

If $\theta$ is an acute angle and $\tan\theta+\cot\theta =2$, Find the value of $\tan ^{7}\theta +\cot ^{7}\theta$.$-2$$1$$2$$0$

7

The expressions $\dfrac{\tan A}{1-\cot A}+\dfrac{\cot A}{1-\tan A}$ can be written as:$\sin A \ \cos A+1$$\sec A \ cosec A+1$$\tan A+ \cot A+1$$\sec A +cosec A$

8

If $x=\cos1^{\circ} \cdot \cos2^{\circ} \cdot \cos3^{\circ}\dots\cos89^{\circ}$ and $y=\cos2^{\circ}\cos6^{\circ}\cos10^{\circ}\dots\cos86^{\circ}$ then what the integer ...

9

If $cosec\theta-\sin\theta=1$ and $\sec\theta-\cos\theta=m$, then $l^{2}m^{2}(l^{2}+m^{2}+3)$ equals to:$1$$2$$2 \sin\theta$$\sin\theta \cos\theta$

10

The angle of elevation of the top of a tower $30$ m high, from two points on the level ground on its opposite sides are $45$ degrees and $60$ degrees. What is the distanc...

11

The number of the real roots of the equation $2\cos (x(x+1))=2^{x}+2^{-x}$ is$2$$1$infinite$0$

12

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process,...

13

A ladder leans against a vertical wall. The top of the ladder is $8$ m above the ground. When the bottom of the ladder is moved $2$ m farther away from the wall, the top ...

14

A vertical tower $\text{OP}$ stands at the centre $\text{O}$ of a square $\text{ABCD}.$ Let $h$ and $b$ denote the lengths $\text{OP}$ and $\text{AB}$ respectively. Suppo...

15

Two vertical lamp-posts of equal height stand on either side of a road $50$ m wide. At a point $\text{P}$ on the road between them, the elevation of the tops of the lamp-...