SSC CGL 24 Aug 2021 Shift 2 Paper

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Question : 55 of 100

Marks: +1, -0

If

\sin ^{2} θ=2 \sin θ-1,0^{∘} ≤ θ ≤ 90^{∘}

, then find the value of

\;{1+cosec θ}/{1-\cos θ}

.

$-2$
1
2
$-1$

Solution:

Given,

\sin ^{2} θ=2 \sin θ-1

⇒ \;\; \sin ^{2} θ-2 \sin θ+1=0

⇒ \;\; \sin ^{2} θ-\sin θ-\sin θ+1=0

⇒ \sin θ(\sin θ-1)-1(\sin θ-1)=0

⇒ \;\; (\sin θ-1)(\sin θ-1)=0

⇒ \;\; \sin θ=1

⇒ \;\; \sin θ=\sin 90^{∘}

θ=90^{∘}

Now,

\;{1+cosec θ}/{1-\cos θ}

=\;{1+cosec 90^{∘}}/{1-\cos 90^{∘}}

[ ∵ θ=90^{∘}]

=\;{1+1}/{1-0} \;\; [\table ∵ , \cos 90^{∘}=0 ; \;\text " and "\; , cosec 90^{∘}=1]

=2

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