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Question

If cosecθcotθ=12,0<θ<π2, then cosθ is equal to

A
53
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B
35
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C
35
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D
53
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Solution

The correct option is B 35
Given: cosecθcotθ=12.....(1)cosecθ+cotθ=2.....(2)(since, cosec2θcot2θ=1)Adding (1) and (2),2cosecθ=12+2=52cosecθ=54sinθ=45sin2θ=16251cos2θ=1625cos2θ=11625=925cosθ=35

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