Question

find the integration

Answer 1

I = sec²x.cosec²x.dx
I = 1.dx/(cos²x.sin²x)
we know ,
sin²x + cos²x = 1 use this here,

I = (sin²x + cos²x)dx/(cos²x.sin²x)
I = dx/cos²x + dx/sin²x
I = sec²x.dx + cosec²x.dx

{ use basic formula ,
sec²x.dx = tanx
cosec²x.dx = - cotx }

I = tanx - cotx + C
where C is constant .