SSC CHSL 12 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

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Question : 53 of 100

Marks: +1, -0

If

3 \cot ^{2} x-7 cosec^{2} x+7=0

, then the value of

x(0 ≤ x ≤ 90^{∘})

is

$30^{∘}$
$0^{∘}$
$90^{∘}$
$60^{∘}$

Solution:

Given,

3 \cot ^{2} x-7 cosec^{2} x+7=0

⇒ 3(cosec^{2} x-1)-7 cosec^{2} x+7=0

⇒ 3 cosec^{2} x-3-7 cosec^{2} x+7=0

⇒ \;\; -4 cosec^{2} x=-4

⇒ \;\; cosec^{2} x=1

⇒ \;\; cosec x=1

Since,

\;\; 0 ≤ x ≤ 90^{∘}

∴ \;\;

cosec

x=cosec 90^{∘}

x=90^{∘}

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