Int cot^(-1) sqrt((1 cosx)/(1-cosx)) dx is equal to

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Int cot^(-1) sqrt((1 cosx)/(1-cosx)) dx is equal to

Last updated at Dec. 27, 2021 by Teachoo Ex 9.4, 1 For each of the differential equations in Exercises 1 to 10, find the general solution : / =(1 - cos )/(1 + cos ) / = (1 - cos )/(1 + cos ) We know that cos 2x = 2cos2 x - 1 Putting x = /2 cos 2 /2 = 2 cos2 /2 - 1 cos x = 2 cos2 /2 - 1 1 + cos x = 2cos2 /2 We know cos 2x = 1 - 2sin2 x

Putting x = /2 cos2 2 /2 = 1 - 2 sin2 /2 cos x = 1 - 2sin2 /2 1 - cos x = 2sin2 /2 Putting values in equation / = ( ^ / )/( ^ / ) = (sin^2 /2 )/cos^(2 ) /2

= tan2 /2 Putting tan2 /2 = sec2 /2 - 1 = ("sec2 " / " - 1" ) Integrating both sides We know that tan2 x + 1 = sec2 x tan2 x = sec2 x - 1 Putting x

= /2 tan2 /2 = sec2 /2 - 1 1 = 1( /-) y = 1 2 /2 - 1 y = /(/) tan / - x + C y = tan / - x + C is the general solution (As 1 2 ( ) = 1/ tan ax + C) Page 2 Last updated at May 29, 2018 by Teachoo Ex 9.4, 2 For each of the differential equations in Exercises 1 to 10, find the general solution :

= 4- 2 -2

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