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Integrate the following w.r.t.x. (sin ...

Integrate the following w.r.t.x.
`(sin (x+a))/(cos (x-b))`

Text Solution

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`intsin(x+a)/(cos (x-b))dx=intsin [dx(x-b)+(a-b)]/(cos (x-b))dx`
`=int[(sin(x-b)cos(a+b)+cos(x-b)sin(a+b))/(cos (x-b))]dx`
`=int[(sin(x-b)cos(a+b))/(cos (x-b))+(cos(x-b)sin(a+b))/(cos(x-b))]dx`
`=int [cos (a+b).tan (x-b)+sin(a+b)]dx`
`=cos(a+b) int tan(x-b)dx+sin(a+b)int 1 dx`
`=cos(a+b).log|sec(x-b)|+[sin (a+b)].x+c`
`=cos(a+b).log|sec (x-b)|+x sin(a+b)+c`
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