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Question

The expression sinA(1+tanA)+cosA(1+cotA) is equivalent to

A
sinA+cosA
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B
secA+tanA
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C
cosec A+cotA
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D
cosec A+secA
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Solution

The correct option is D cosec A+secA
sinA(1+tanA)+cosA(1+cotA)
=sinA(1+sinAcosA)+cosA(1+cosAsinA)
=sinAcosA(cosA+sinA)+cosAsinA(sinA+cosA)
=(cosA+sinA)(sinAcosA+cosAsinA)
=(cosA+sinA)(sin2A+cos2AsinAcosA)
=cosA+sinAsinAcosA
=1sinA+1cosA
=cosec A+secA

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