SSC CGL 10 Aug 2017 Shift 1 Paper

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Question : 71 of 100

Marks: +1, -0

If 2 cos θ =2 - sin θ, then what is the value of cos θ ?

1 or $3/5$
1 or $-1/2$
-1 or $-1/2$
-1 or $3/5$

Solution:

2\cos θ = 2 -\sinθ

=>

\sinθ = 2 -2 \cos θ

On squaring both sides,

\sin^2 θ = 4 + 4 \cos^2 θ - 8 \cosθ

⇒

1 - \cos^2 θ =4 +4\cos^2θ- 8 \cos θ

⇒

5 \cos^2θ - 8 \cos θ + 3 = 0

⇒

5 \cos^2θ - 5 \cos θ -3 \cos θ + 3= 0

⇒

5 \cosθ (\cosθ -1 ) - 3 (\cos θ-1 ) = 0

⇒

(\cos θ -1 ) (5 \cos θ - 3 ) = 0

\cos θ = 1,3/5

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