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

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

Text Solution

Verified by Experts

`1/(1-sin(x/2)) = 1/(1-sin(x/2)) **(1+sin(x/2))/(1+sin(x/2)) `
`=(1+sin(x/2))/(1-sin^2(x/2))`
`=(1+sin(x/2))/(cos^2(x/2))`
`=sec^2(x/2)+tan(x/2)sec(x/2)`
`:. int 1/(1-sin(x/2))dx = int (sec^2(x/2)+tan(x/2)sec(x/2)) dx`
`=2tan(x/2)+2sec(x/2)+c`
`=2(tan(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 int(1)/(1+sinx)dx .

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

(i) int (cosx)/(1+cosx)dx , (ii) int (sinx)/((1-sinx))dx

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

Evaluate: int1/(cosx-sinx)\ dx

Let f(x) = ln ((1-sinx)/(1+sinx)) , then show that int_(a)^(b) f(x)dx = int_(b)^(a) ln((1+sinx)/(1-sinx))dx .