If e^y=tanx, 0<x<pi/2 what is dy/dx in terms of x?

Question

A.secxcscx
B.sec^2x
C.secx
D.sin x sec x

Answer 1

e^y=tanx

e^y dy/dx = sec^2 x
dy/dx = sec^2 x / e^y , but e^y = tanx
= sec^2 x / tanx
= 1/cos^2 x * cosx/sinx
= 1/(sinx cosx)
or
cscx secx , choice A

Answer 2

How did you get from sec^2 x / tanx to 1/cos^2 x * cosx/sinx