SSC CGL 10 Jun 2019 Shift 1 Paper

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Question : 68 of 100

Marks: +1, -0

If

3 \sin \θ=2 \cos ^{2} \θ, 0° < \θ < 90°,

then the value of

\ (\tan ^{2} \θ+\sec ^{2} \θ-\ {\cosec}^{2} \θ\ )

is :

-2
$-7/3$
$7/3$
2

Solution:

3 \sin \θ=2 \cos ^{2} \θ

\θ=30°

satisfies
So,

\tan ^{2} \θ+\sec ^{2} \θ-\ {\cosec}^{2} \θ

=\tan ^{2} 30+\sec ^{2} 30-\ {\cosec}^{2} 30

=\ {1}/{3}+\ {4}/{3}-4=-\ {7}/{3}

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