If $0<\alpha <\frac{\pi }{6}$, then $\alpha \left(\mathrm{cosec}\alpha \right)$ is

Important Questions on Trigonometric Ratios and Identities

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $\sec \theta =\frac{13}{12},\theta$ lies in $4^{\text{th }}$quadrant, then $\tan \theta \times \mathrm{cosec}\theta \times \sin \theta \times \cos \theta =$

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $\cos \left({\theta }_1\right)+\cos \left({\theta }_2\right)+\cos \left({\theta }_3\right)+\cos \left({\theta }_4\right)=-4,$ then the value of $\cot \left(\frac{{\theta }_1}{2}\right)+\cot \left(\frac{{\theta }_2}{2}\right)+\cot \left(\frac{{\theta }_3}{2}\right)+\cot \left(\frac{{\theta }_4}{2}\right)=$
 

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

$\tan 1°\times \tan 2°\times \tan 3°\times \cdots \cdots \cdots \cdots \times \tan 89°=$

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $\cos \theta =-\frac{\sqrt{3}}{2}$ and $\sin \alpha =-\frac{3}{5}$, where $\theta$ does not lie in the third quadrant, then $\frac{2\tan \alpha +\sqrt{3}\tan \theta }{{\cot }^2\theta +\cos \alpha }$ is equal to

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

What is the value of $\left(\frac{1}{\sqrt{3}} + \cos {60}^0\right)?$

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The graphs of the polynomial $x^2-1$ and $\cos x$ intersect

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The value of ${\sin }^{2}51°+{\sin }^{2}39°$ is

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $5\cos \theta -12\sin \theta =0$, then what is the value of $\frac{1+\sin \theta +\cos \theta }{1-\sin \theta +\cos \theta }$?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

$∆ABC$is right angled at $B$.$\cos A = \frac{8}{17}$ . If what is the value of $cot C$?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $\tan \theta =\frac{2}{3}$, then $\frac{3 \sin \theta -4 \cos \theta }{3 \sin \theta +4 \cos \theta }$ is equal to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The value of $\frac{\tan 330° \sec 420° \sin 300°}{\tan 135° \sin 210° \sec 315°}$ is equal to

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

What is the value of $\left(\frac{1}{2}-\sec {30}^{\text{o}}\right)$? 

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The number of solutions of the equation $\left|\cot x\right|=\cot x+\frac{1}{\sin x},0\le x\le 2\pi$

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $A=\left\{x\in [0,2\pi ]/\tan x-{\tan }^{2}x>0\right\}$ and $B=\left\{x\in [0,2\pi ]/\left|\sin x\right|<\frac{1}{2}\right\},$ then $\mathrm{A}\cap \mathrm{B}=$

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If A lies in the first quadrant  and $6 \tan A=5$, then the value of $\frac{8 \sin A-4 \cos A}{\cos A+2 \sin A}$ is:

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The value of $\frac{1-2{\sin }^2{\mathrm{\theta cos}}^2\mathrm{\theta }}{{\sin }^4\mathrm{\theta }+{\cos }^4\mathrm{\theta }}-1$is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

If $7 {\cos }^2\mathrm{\theta }+3 {\sin }^2\mathrm{\theta }=6, 0^{\circ }<\mathrm{\theta }<{90}^{\circ }$, then the value of $\frac{{\cot }^{2}2\mathrm{\theta }+{\sec }^{2}2\mathrm{\theta }}{{\tan }^{2}2\mathrm{\theta }-{\sin }^{2}2\mathrm{\theta }}$ is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

$\underset{x\to 0}{\lim }\frac{1-\cos nx}{1-\cos mx}=$

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

What is the value of $\left(\tan {30}^{\text{o}}+\frac{\sqrt{3}}{2}\right)$?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Trigonometric Functions and Properties

The angle of elevation of the top of a vertical tower from a point A, due east of it is ${45}^o$ . The angle of elevation of the top of the same tower from a point B, due south of A is ${30}^o$ . If the distance between A and B is $54\sqrt{2}m$ , then the height of the tower (in meters), is: