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प्रश्न
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
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उत्तर
Let `"I" = int cos("x + a")/sin("x +b")"dx".` Then
`"I" = cos("x"+"b"+"a" -"b")/sin("x+b")"dx"`
`"I" = int cos{("x+b")+ ("a"- "b")}/sin("x+b")"dx"`
`"I" = int (cos("x+b").cos("a"-"b")-sin("x+b").sin("a"-"b"))/sin("x+b")"dx"`
`"I" = int [cos("a"-"b") . cot ("x+b") - sin("a"-"b")]"dx"`
`"I" = cos("a"-"b") . log |sin("x + b")| - "x".sin("a" - "b")`
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