If tan θ = - frac{1}{{√ {10} }} and θ lies in fourth quadrant, then cos θ =

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3.Trigonometrical Ratios, Functions and Identities

easy

If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $

A

$1/\sqrt {11} $

B

$ - 1/\sqrt {11} $

C

$\sqrt {\frac{{10}}{{11}}} $

D

$ - \sqrt {\frac{{10}}{{11}}} $

Solution

(c) We have $\tan \theta = – \frac{1}{{\sqrt {10} }},$

therefore $\theta $ is in $IV$ quadrant.

So $\cos \theta = + ve$.Now $1 + {\tan ^2}\theta = {\sec ^2}\theta $

$\Rightarrow 1 + \frac{1}{{10}} = {\sec ^2}\theta $

$ \Rightarrow {\sec ^2}\theta = \frac{{11}}{{10}}$

$\Rightarrow \cos \theta = \sqrt {\left( {\frac{{10}}{{11}}} \right)} $.

Standard 11

Mathematics

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(KVPY-2010)