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Question

If π2<α<π, then 1cosα1+cosα+1+cosα1cosα=

A
2secα
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B
2secα
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C
2cosecα
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D
2cosecα
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Solution

The correct option is D 2cosecα

1cosα1+cosα+1+cosα1cosα


=(1cosα)2sin2α+(1+cosα)2sin2α


=|cosecαcotα|+|cosecα+cotα|


=2cosecα because sinα>0,α(π2,π)


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