Advertisements
Advertisements
Question
`int("I" - cosx)"cosec"^2x"d"x` = ______.
Options
`- 2 cot (x/2) + "c"`
`- cot (x/2) + "c"`
`2tan (x/2) + "c"`
`tan(x/2) + "c"`
MCQ
Fill in the Blanks
Advertisements
Solution
`int("I" - cosx)"cosec"^2x"d"x` = `tan(x/2) + "c"`.
Explanation:
`int("I" - cosx)"cosec"^2x"d"x`
= `int "cosec"^2x "d"x - int cot x "cosec" x "d"x`
= `- cot x + "cosec" x + "c"`
= `(1 - cos x)/sinx + "c"`
= `(2sin^2 x/2)/(2sin x/2 cos x/2) + "c"`
= `tan(x/2) + "c"`
shaalaa.com
Integrals of Trignometric Functions
Is there an error in this question or solution?
