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Question

If 3π4<α<π, then 2cotα+1sin2α is equal to

A
1cotα
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B
1+cotα
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C
1+cotα
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D
1cotα
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Solution

The correct option is B 1cotα
2cotα+1sin2α=2cotα+cosec2α

=2cotα+1+cot2α=|1+cotα|=1cotα

( Since cotα<1 when 3π4<α<π),

|1+cotα|=1cotα

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