SSC CGL Tier II 12 Apr 2015 Paper

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Question : 45 of 100

Marks: +1, -0

If

\tan \α = 2

, then the value of

{\cosec ^{2} \α-\sec ^{2} \α}/{\cosec ^{2} \α+\sec ^{2} \α}

is

$-15/9$
$-3/5$
$3/5$
$17/5$

Solution:

(2)

\tan \α = 2

∴

{\cosec ^{2} \α-\sec ^{2} \α}/{\cosec ^{2} \α+\sec ^{2} \α}

= {1+\cot ^{2} \α-1-\tan ^{2} \α}/{1+\cot ^{2} \α+1+\tan ^{2} \α }

= { \cot ^{2} \α- \tan ^{2} \α}/{ \cot ^{2} \α+ \tan ^{2} \α +2}

= { {1}/{4}-4}/{ {1}/{4}+4+2}= { {1-16}/{4}}/{ {1+16+8}/{4}}

= {-15}/{25}= {-3}/{5}

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