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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 D

1cotα


1cotα

We have:

=2cotα+1sin2α

=2cosαsinα+1sin2α

=2sinαcosα+sin2α+cos2αsin2α

=(sinα+cosα)2sin2α

=(1+cotα)2

=|1+cotα|

=(1+cotα)[When3π4<α<π,cotα<1cotα+1<0]

=1cotα


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