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Question

1+cosAsinA1+cosA+sinA=secAtanA=1sinAcosA=1sinA1+sinA

A
True
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B
False
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C
Ambiguous
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D
Data insufficient
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Solution

The correct option is B True
1+cosAsinA1+cosA+sinA
=(1+cosAsinA)2(1+cosA)2sin2A
=1+cos2A+sin2A2cosAsinA2sinA+2cosA(1+cosA)2(1cosA)(1+cosA)
=22cosAsinA2sinA+2cosA(1+cosA)(1+cosA1+cosA)
=2(1+cosAsinAsinA+cosA)2cosA(1+cosA)
=1+cosAsinAsinA+cosAcosA(1+cosA)
=(1+cosA)sinA(1+cosA)cosA(1+cosA)
=secAtanA
=1sinAcosA
=(1sinA)2cos2A
=(1sinA)21sin2A
=(1sinA)1+sinA

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