3.Trigonometrical Ratios, Functions and Identities
easy

यदि $\tan \theta  =  - \frac{1}{{\sqrt {10} }}$ तथा $\theta $ चतुर्थ चतुर्थाश में हो, तो $\cos \theta  = $

A

$1/\sqrt {11} $

B

$ - 1/\sqrt {11} $

C

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

D

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

Solution

$\tan \theta  =  – \frac{1}{{\sqrt {10} }},$अत: $\theta $, $IV$ चतुर्थांश में है।

अत: $\cos \theta  = $ धनात्मक.

अब $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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