Home
Class 12
MATHS
Evaluate: int1/(sin(x-a)s in(x-b))dx...

Evaluate: `int1/(sin(x-a)s in(x-b))dx`

A

`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

  • INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|3 Videos

  • INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer|13 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT EXEMPLAR ENGLISH|Exercise Objective|1 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|18 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int1/(sin(x-a)sin(x-b))\ dx

Evaluate: int1/(sin(x-a)sin(x-b))\ dx

Evaluate: int1/(sin(x-a)sin(x-b))dx

Evaluate: int1/(sin(x-a)sin(x-b))dx

Evaluate: int1/(sin(x-a)cos(x-b))\ dx

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

Evaluate: int1/(cos(x-a)cos(x-b))\ dx

Evaluate : int(sin(x-a))/(sin(x+a))dx

Evaluate : int(sin(x-a))/(sin(x+a))dx

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