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Question

If 2sin2θ=3cosθ, where 0θ2π, then θ=

A
π6,7π6
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B
π3,5π3
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C
π3,7π3
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D
None of these
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Solution

The correct option is A π3,5π3
Given: 2sin2θ=3cosθ

2(1cos2θ)=3cosθ

2cos2θ+3cosθ2=0

2cos2θ+4cosθcosθ2=0

(2cosθ1)(cosθ+2)=0

cosθ=12 and cosθ=2 is not possible because cosθ1

cosθ=12

θ=π3,5π3

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