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प्रश्न
Evaluate:
`int sin(x + a)/cos(x - b)dx`
मूल्यांकन
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उत्तर
`int sin(x + a)/cos(x - b)dx`
= `intsin[(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[tan(x - b) * cos(a + b) + sin(a + b)]dx`
= `cos(a + b) inttan(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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