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Question

The numerical value of cosec θ[1cosθsinθ+sinθ1cosθ]2cot2θ is

A
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B
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C
2
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3
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Solution

The correct option is C 2
cosec θ[1cosθsinθ+sinθ1cosθ]2cot2θ=[1cosθsin2θ+11cosθ]2cot2θ=[1cosθ1cos2θ+11cosθ]2cot2θ=[11+cosθ+11cosθ]2cot2θ=[1+cosθ+1cosθ1cos2θ]2cot2θ=2 cosec 2θ2cot2θ=2

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