Evaluate $\sin {132}^{\circ }\times \sin {12}^{\circ }$

Important Questions on Trigonometric Functions

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $\cos 1200°+\tan 1485°$ is

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

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

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

If $x=\cos 1°\cos 2°\cos 3°\dots \cos 89°$ and $y=\cos 2°\cos 6°\cos 10°\dots \cos 86°,$ then what is the integer nearest to $\frac{2}{7}{\log }_2\left(\frac{y}{x}\right)?$ 

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

For any $\theta \in \left(\frac{\pi }{4},\frac{\pi }{2}\right),$ the expression $3{\left(\sin \theta -\cos \theta \right)}^4+6{\left(\sin \theta +\cos \theta \right)}^2+4 {\mathrm{s}\mathrm{i}\mathrm{n}}^6\theta$ equals:

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $\mathrm{s}\mathrm{i}\mathrm{n}10°\mathrm{s}\mathrm{i}\mathrm{n}30°\mathrm{s}\mathrm{i}\mathrm{n}50°\mathrm{s}\mathrm{i}\mathrm{n}70°$ is:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $2\sin \left(\frac{\mathrm{\pi }}{8}\right)\sin \left(\frac{2\mathrm{\pi }}{8}\right)\sin \left(\frac{3\mathrm{\pi }}{8}\right)\sin \left(\frac{5\mathrm{\pi }}{8}\right)\sin \left(\frac{6\mathrm{\pi }}{8}\right)\sin \left(\frac{7\mathrm{\pi }}{8}\right)$ is :

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

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

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}$ is 

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The equation $y=\sin x·\sin \left(x+2\right)-{\sin }^2(x+1)$ represents a straight line lying in:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of ${\cos }^{2}10°–\cos 10°\mathrm{ }\cos 50°+\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}50°$ is

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The range of the function $f\left(x\right)={\log }_{\sqrt{5}}\left(3+\cos \left(\frac{3\pi }{4}+x\right)+\cos \left(\frac{\pi }{4}+x\right)+\cos \left(\frac{\pi }{4}-x\right)-\cos \left(\frac{3\pi }{4}-x\right)\right)$ is :

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

In a $\mathrm{\Delta }ABC$, $\frac{a}{b}=2+\sqrt{3}$, and $\angle C=60°.$ Then the ordered pair $(\angle A,\angle B)$ is equal to:

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

$\cot \frac{\pi }{16}· \cot \frac{2\pi }{16}· \cot \frac{3\pi }{16}· \cot \frac{4\pi }{16}· \cot \frac{5\pi }{16}· \cot \frac{6\pi }{16}· \cot \frac{7\pi }{16}=$

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $\tan 1°\tan 2°\tan 3°\dots \tan 89°$ is

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

${\left(\frac{\sin 35°}{\cos 55°}\right)}^2+{\left(\frac{\cos 55°}{\sin 35°}\right)}^2-2\cos 30°=$

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

If $\tan 15°+\frac{1}{\tan 75°}+\frac{1}{\tan 105°}+\tan 195°=2\mathrm{a}$, then the value of $\left(a+\frac{1}{a}\right)$ is :

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The value of $\tan \left(\frac{7\pi }{8}\right)$ is

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

If $cosec\theta +\cot \theta =\frac{1}{3},$ then $\theta$ lies in the

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

If $\mathrm{c}\mathrm{o}\mathrm{s}\left(\alpha +\beta \right)=\frac{3}{5}\mathrm{ },\sin (\alpha -\beta )=\frac{5}{13}$ and $0<\alpha ,\beta <\frac{\pi }{4},$ then $\tan \left(2\alpha \right)$ is equal to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Functions of Sum and Difference of Two Angles

The expression $\frac{\mathrm{tanA}}{1-\mathrm{cotA}}+\frac{\mathrm{cotA}}{1-\mathrm{tanA}}$ can be written as :