SSC CHSL 16 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

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Question : 69 of 100

Marks: +1, -0

If

\sin θ=\;{12}/{13}

, then

\;{\sin ^{2} θ-\cos ^{2} θ}/{2 \cos θ \sin θ} × \cot ^{2} θ=?

$\;{595}/{1152}$
$\;{119}/{864}$
$\;{119}/{144}$
$\;{595}/{3456}$

Solution:

Given,

\sin θ=\;{12}/{13}

∴ \;\; \cos ^{2} θ=1-\sin ^{2} θ

\;\; =1-(\;{12}/{13})^{2}

\;\; =\;{169-144}/{169}=\;{25}/{169}

\cos θ \;\; =√{\;{25}/{169}}=\;{5}/{13} \;\text " and "\;

\cot θ=\;{\cos θ}/{\sin θ} \;\; =\;{\;{5}/{13}}/{{12}/{13}}=\;{5}/{12}

Now, the value of

\;{\sin ^{2} θ-\cos ^{2} θ}/{2 \cos θ \sin θ} × \cot ^{2} θ

=\;{({12}/{13})^{2}-({5}/{13})^{2}}/{2 × \;{5}/{13} × \;{12}/{13}} ×(\;{5}/{12})^{2}

=\;{\;{144-25}/{169}}/{{120}/{169}} × \;{25}/{144}=\;{119}/{120} × \;{25}/{144}

=\;{595}/{3456}

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