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Icosecd∫(I-cosx)cosec2xdx = ______.

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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
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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"`

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Integrals of Trignometric Functions
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