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ज्ञात करें int(dx)/(sin(x-alpha)sin(x-be...

ज्ञात करें `int(dx)/(sin(x-alpha)sin(x-beta))`

लिखित उत्तर

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`I=1/(sin(beta-alpha))int(sin{(x-alpha)-(x-beta)})/(sin(x-alpha)sin(x-beta))dx`
`=1/(sin(beta-alpha))int(sin(x-alpha)cos(x-beta)-cos(x-alpha)sin(x-beta))/(sin(x-alpha)sin(x-beta))dx`
`=1/(sin(beta-alpha))int[cot(x-beta)-cot(x-alpha)]dx`
`=1/(sin(beta-alpha))[log[sin(x-beta)|-log|sin(x-alpha)|]+c`
`=1/(sin(beta-alpha))"log"|(sin(x-beta))/(sin(x-alpha))|+c`
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