The general value of \theta satisfying the equation 2 \sin ^{2} \theta-3 \sin \theta-2=0, is

Correct Answer is : nπ+(−1)n7π6

NIMCET 2011 Question Paper with solutions

Question : 15 of 120

Marks: +1, -0

The general value of

θ

satisfying the equation

2 \sin ^{2} θ-3 \sin θ-2=0

, is

Solution:

Given,

2 \sin ^{2} θ-3 \sin θ-2=0

⇒ 2 \sin ^{2} θ-4 \sin θ+\sin θ-2=0

⇒ 2 \sin θ⟨\sin θ-2+1(\sin θ-2)=0

⇒ (\sin θ-2)(2 \sin θ+1)=0

⇒ \sin θ=- {1}/{2}, \sin θ ≠ 2 \;\;( ∵ -1 ≤ \sin θ ≤ 1)

⇒ θ=n π+(-1)^{n}(\;{7 π}/{6})

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