Home
Class 12
MATHS
int sinx/sin(x-alpha)dx=Ax+B log (sin(x-...

`int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C` then find out `A & B`

Text Solution

Verified by Experts

`"Let " x- a=t`
`rArr " "dx=dt`
`int(sinx)/(sin(x-a)) dx= int(sin (t+a))/(sin t) dt`
`= int (sin t cos a + cos t sin a)/(sin t)dt``=int (cos a +sin a cot t) dt`
` = cos a int 1 dt + sin a int cot t dt`
`= t cos a+ sin a log |sin t|+c_(1)`
`=(x-a) cos a`
`+sin a . log |sin (x-a)|+C_(1)`
`=x cos a + sin a log `
`|sin (x-a)|+C_(1)-a cos a`
`=x cos a + sin a log |sin (x-a)|+C`
`" where " c=c_(1) -a cos a`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.11|21 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int(sin x)/(sin(x-alpha))dx=Ax+B log(sin(x-alpha))+C then find out A&B

If int(sinx)/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+c then

int(sin x)/(sin(x+alpha)dx)

If int(sin x)/(sin(x-alpha))dx=Ax+B log sin(x-alpha) , then value of (A,B) is

If int (sin x)/(sin (x-alpha))dx =Ax+B log sin (x-alpha)+C , then the value of (A,B) , is

If intsinx/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+C , then value of (A,B) is (A) (-sinalpha,cosalpha) (B) (-cosalpha,sinalpha) (C) (sinalpha,cosalpha) (D) (cosalpha,sinalpha)

If int (sin x)/(sin (x-a))dx =Ax +B log sin (x-alpha ) +C, then value of (A,B) is:

int(sinx+cosx)/(sin(x+alpha))dx=

int(sin2x)/(sin(x-alpha)sin(x+alpha))dx

int sqrt((sin(x-alpha))/(sin(x+alpha)))