Home
Class 12
MATHS
int1/(1-sinx/2)\ dx...

`int1/(1-sinx/2)\ dx`

Text Solution

Verified by Experts

`int1/(1-sinx/2)\ dx`

Multiplying by its conjugate numerator and denominator

`=int(1+sinx/2)/((1+sinx/2)(1-sinx/2))\ dx`

`=int(1+sinx/2)/(1-sin^2(x/2))\ dx`

`=int(1+sinx/2)/(cos^2(x/2))\ dx`

`=int(sec^2(x/2)+tan(x/2)sec(x/2))\ dx`

`=2tan^2(x/2)+2sec(x/2))+C`

Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

int(1)/(1-sinx) dx

Evaluate : int(tan^(2)x)dx Evalauate: int1/(1+sinx) dx

Evaluate: int1/(cosx-sinx)\ dx

Evaluate: int1/(sinx+cosx)\ dx

Evaluate int(1)/(1+sinx)dx .

int ((1+ sinx))/((1- sinx)) dx=?

If int(1)/(1+sinx)dx=tan((x)/(2)+a)+b then