# Integral sec^2(x)/cosec^2(x)

69 Points
13 years ago

dear anitha

it will become integral{(tan(x))^2}dx

integral   {(tan(x))^2}dx

= integral   {(sec(x))^2 - 1}dx       [since tan^2(x)+1=sec^2(x)]

= 1/2( tan(x)) -1        [integral{sec^2(x)=tanx]

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IIT Bombay

AKASH GARG
30 Points
13 years ago

tan^2x=sec^2x-1

integrate it,

=> tanx-x                   ans.

subhangee sahoo
18 Points
12 years ago

integration sec^2(x)/cosec^2(x)

= intg 1/cos^2(x)/1/sin^2(x)

= intg tan^2(x)

=intg sec^2(x)- intg dx

=tanx-x+c

Rishi Sharma
askIITians Faculty 646 Points
4 years ago
Dear Student,
Please find below the solution to your problem.

it will becomeintegral{(tan(x))^2}dx
integral {(tan(x))^2}dx
= integral {(sec(x))^2 - 1}dx [since tan^2(x)+1=sec^2(x)]
= 1/2( tan(x)) – X +C [integral{sec^2(x)=tanx]

Thanks and Regards