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Question

dxsin x.sin(x+α) is equal to


  1. cosec α logsin xsin(x+α)+C

  2. cosec α logsin(x+α)sin x+C

  3. cosec α logsec(x+α)sec x+C

  4. cosec α logsec xsec(x+α)+C


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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