IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

sharwari

plz help me to solve this question:

cos2x/sinx

puneet

Put cos 2x = 1 / t

So, dx = dt / ( 2t². sin 2x)

so,

cos2x/sinx =

dt / ( 2t². 2sin²x) *

t * cosx

=

dt /

2 * t(t-1)

t+1

Now put t + 1 = p²

So,

cos2x/sinx =

2* dp / (p² - 1)*( p² - 2 )

=

2* dp / ( p² - 2 ) -

2* dp / ( p² - 1 )

Now these integrals can be easily intergated and thus we are done by resubstituting the values of p.

Cheers !!!!!!!!!!!!