Home
Class 12
MATHS
int (dx)/(sin(x-a)sin(x-b)...

`int (dx)/(sin(x-a)sin(x-b)`

A

`1/sin(b-a)log|(sin(x-b))/(sin(x-a))|+C`

B

`cosec(b-a)log|(sin(x-a))/(sin(x-b))|+C`

C

`cosec(b-a)log|(sin(x-b))/(sin(x-a))|+C`

D

`sin(b-a)log|(sin(x-a))/(sin(x-b))|+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`I = int(dx)/(sin(x-a)sin(x-b))`
`= (1)/(sin(b-a))int(sin(b-a))/(sin(x-a)sin(x-b))dx`
`= (1)/(sin(b-a))int(sin(x-a-x+b))/(sin(x-a)sin(x-b))dx`
`= (1)/(sin(b-a))int(sin{(x-a)-(x-b)})/(sin(x-a)sin(x-b))dx`
`= (1)/(sin(b-a)) int(sin(x-a)cos(x-b)-cos(x-a)sin(x-b))/(sin(x-a)sin(x-b))dx`
`= (1)/(sin(b-a)) int[cot(x-b)-cot(x-a)]dx`
`= (1)/(sin(b-a)) [log|sin(x-b)|-log|sin(x-a)|]+C`
`= cosec (b-a)log|(sin(x-b))/(sin(x-a))|+C`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    NCERT EXEMPLAR|Exercise Differential Equations|77 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT EXEMPLAR|Exercise Inverse Trigonometric Functions|55 Videos

Similar Questions

Explore conceptually related problems

int(dx)/(cos(x-a)sin(x-b))=

If int(k)/(sin(x-a)sin(x-b))dx=log[(sin(x-a))/(sin(x-b))]+c, then k=

Evaluate: int(1)/(sin(x-a)sin(x-b))dx

Evaluate: int(1)/(sin(x-a)sin(x-b))dx

int (dx) / (sin x sin2x)

int(sin(x+a)-sin(x-a))/(sin(x+a)+sin(x-a))dx=

If int(k)/(sin(x-a)cos(x-b))dx=log[(sin(x-a))/(cos(x-b))]+c , then k=

int(dx)/((sin x+sin 2x))