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Question

The number of values of θ in [0,2π]that satisfy the equation sin2θcosθ14


A

1

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B

2

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C

3

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D

4

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Solution

The correct option is B

2


sin2θcosθ=14(1cos2θ)cosθ= 1444cos2θ4cosθ=14 cos2θ+4cosθ3=04 cos2θ+6cosθ2 cosθ3=02cosθ(2cosθ+3)1(2cosθ+3)=0(2 cosθ+3)(2cosθ1)=02 cosθ+3=0 or ,2cosθ1=0cosθ=32 or cos θ=12Here,cosθ=32 is not possible. cosθ=12cosθ=cos π3θ=2nπ± π3Now for n=0 and 1,the values of θ are π3,5π3 and 7π3,but 7π3 is not in [o,2π]Hence,there are two solutinos in[o,2π].


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