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\int \left ( \tan ^{2} x +\cot ^{2}x\right )dx

  • Option 1)

    \tan x + \cot x +C

  • Option 2)

    \tan x + \cot x -2+C

  • Option 3)

    \tan x + \cot x -2x +C

  • Option 4)

    \sec x + \csc x+C

 

Answers (1)

best_answer

As we have learned

Integration of trigonometric function of power m -

\int tan^{m}xdx , \int cot^{m}xdx

 

 

- wherein

for m=2

use tan^{2}x=sec^{2}x-1  , cot^{2}x=cosec^{2}x-1

 

\int \left ( \sec ^{2} x -1+ \csc ^{2} x-1\right )dx

\int \left ( \sec^{2} + \csc^{2}x -2\right )dx 

\tan x + \cot x -2x+C

 

 

 

 

 


Option 1)

\tan x + \cot x +C

This is incorrect

Option 2)

\tan x + \cot x -2+C

This is incorrect

Option 3)

\tan x + \cot x -2x +C

This is correct

Option 4)

\sec x + \csc x+C

This is incorrect

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