(C) Given that $\tan \theta = \frac{20}{21}$.We know that $\sec^2 \theta = 1 + \tan^2 \theta$.$\sec^2 \theta = 1 + (\frac{20}{21})^2 = 1 + \frac{400}{

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(C) Given that $\tan \theta = \frac{20}{21}$.We know that $\sec^2 \theta = 1 + \tan^2 \theta$.$\sec^2 \theta = 1 + (\frac{20}{21})^2 = 1 + \frac{400}{441} = \frac{441 + 400}{441} = \frac{841}{441}$.Therefore,$\sec \theta = \pm \sqrt{\frac{841}{441}} = \pm \frac{29}{21}$.Since $\cos \theta = \frac{1}{\sec \theta}$,we have $\cos \theta = \pm \frac{21}{29}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

Easy

If $\tan \theta = \frac{20}{21}$,then $\cos \theta$ will be

A
$\pm \frac{20}{41}$
B
$\pm \frac{1}{21}$
C
$\pm \frac{21}{29}$
D
$\pm \frac{20}{21}$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

$\operatorname{Tanh}^{-1}(\sin \theta) =$

MediumAP EAMCET 2025

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If $x = \sin 130^\circ \cos 80^\circ$,$y = \sin 80^\circ \cos 130^\circ$,and $z = 1 + xy$,which one of the following is true?

Easy

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If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$,then $\sin \alpha + \cos \alpha$ and $\sin \alpha - \cos \alpha$ are equal to:

Medium

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If $\sin (A + B) = 1$ and $\cos (A - B) = \frac{\sqrt{3}}{2}$,then the smallest positive values of $A$ and $B$ are

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$\frac{\cos 10^{\circ} + \cos 80^{\circ}}{\sin 80^{\circ} - \sin 10^{\circ}} = ?$

EasyAP EAMCET 2024

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If $\tan \theta = \frac{20}{21}$,then $\cos \theta$ will be

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