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Question

dxsin x.sin(x+α) is equal to


A

cosec α logsin xsin(x+α)+C

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B

cosec α logsin(x+α)sin x+C

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C

cosec α logsec(x+α)sec x+C

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D

cosec α logsec xsec(x+α)+C

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Solution

The correct option is A

cosec α logsin xsin(x+α)+C


dxsin x.sin(x+α)=1sinαsin((x+α)x)sin x.sin(x+α)dx=cosec α(sin(x+α)cos xcos(x+α)sin x)sin x.sin(x+α)dx=cosec α[cot xcot(x+α)]dx=cosec α[log sin xlog sin(x+α)]+C=cosec α logsin xsin(x+α)+C



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