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Question

What is 1+sinA1sinA1sinA1+sinA equal to ?

A
secAtanA
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B
2secA.tanA
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C
4secA.tanA
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D
4cosec A.cotA
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Solution

The correct option is C 4secA.tanA
(1+sinA)(1sinA)(1sinA)(1+sinA)=(1+sinA)(1+sinA)(1sinA)(1sinA)(1sinA)(1+sinA)=(1+2sinA+sin2A)(12sinA+sin2A)(1sin2A)
=4sinAcos2A ......... [1sin2A=cos2A]
=4tanAsecA
Hence, C is correct.

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