`int(sin(x-alpha))/(sin(x+alpha))dx` का मान ज्ञात कीजिए।

Explanation

माना `I = int(sin(x -alpha))/(sin(x+alpha))dx`
माना ` x + alpha = t " "rArr x = t - alpha rArr dx = dt`
`therefore" "I int (sin(x-alpha))/(sin t)dt`
` = int [(sin t cos 2alpha)/(sin t) - (cos t sin 2alpha)/(sin t)]dt `
` = int cos 2alpha dt - int sin2alpha cot t dt`
`=cos2alpha int dt - sin 2alpha int cot t dt `
`= t cos 2alpha - sn 2 alpha log|sin t|+c`
`=(x+alpha) cos2alpha - sin 2 alpha log|sin (x +alpha)|+c`
`= x cos 2 alpha - sin 2 alpha log|sin (x + alpha )|+c_(1)`
जहाँ` c_(1) = c + alpha cos 2alpha`