SSC CGL 5 Aug 2017 Shift 1 Paper

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Question : 71 of 100

Marks: +1, -0

If

\cos^2 θ -\sin θ = 1/4

, then what is the value of sin θ ?

$- 1$
$1/2$
1
$3/2$

Solution:

\cos^2 θ -\sin θ = 1/4

⇒

1- \sin ^2θ- \sin θ = 1/4

⇒

4 - 4 \sin ^2 θ -4 \sin θ= 1

⇒

4 \sin^2 θ + 4 \sin θ - 3 = 0

⇒

4\sin^2θ + 6\sinθ - 2 \sin θ-3=0

⇒

2 \sin θ(2 \sin θ + 3) -1 (2 \sin θ+ 3 ) = 0

⇒

(2 \sin θ + 3) (2 \sin θ - 1 ) = 0

⇒

2 \sin θ - 1 = 0

∴

\sin θ= 1/ 2

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