Question

Step By step show integration plzz

Answer 1

\[\int\limits_{?}^{?}\frac{ (\sec(x))^2 }{ (cosec(x))^2 }\]

Answer 2

try converting everything into sin and cos
see if it helps simplifying the function to be integrated

Answer 3

sec x= ...
cosec x = ..?

Answer 4

1/cosx and 1/sinx

Answer 5

i know trigonometry and rules of integration but ia m not able to do it.

Answer 6

Right, because what we have is

\[\large \frac{\frac{1}{cos^2(x)}}{\frac{1}{sin^2(x)}}\]

which comes out to \[\large \frac{sin^2(x)}{cos^2(x)}\]

Which we know to be

\[\large \tan^2(x)\]

This integral looks alot better like

\[\large \int^{}_{} tan^2(x)dx\]

Answer 7

so basically you just need integration of tan^2 x , right ?

Answer 8

oh he showed you

Answer 9

now use the pythagorean identity involving tan^2 x

Answer 10

sec^2(x)-1

Answer 11

Right...

Answer 12

yes,
and you know the integration of sec^2 x
?
pretty standard

Answer 13

tanx

Answer 14

thats correct
and you must also be knowing integration of 1

Answer 15

x

Answer 16

Ty

Answer 17

welcome :)

Answer 18

No problem :)