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Question

For all values of α the given expression is equal to:
(sinα+cosecα)2+(cosα+secα)2(tan2α+cot2α)

A
0
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B
2
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C
4
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D
7
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Solution

The correct option is D 7
(sinα+cosecα)2+(cosα+secα)2(tan2α+cot2α)
=sin2α+cosec2α+2+cos2α+sec2α+2tan2αcot2α
=4+sin2α+cos2α+sec2αtan2α+cosec2αcot2α=7

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