Question

Prove`(sin^2A/cosA)-(cos^2A/sinA)=(secA/csc^2A)-(cscA/sec^2A)`?

Answer 1

`LHS=(sin^2A/cosA)-(cos^2A/sinA)`

`=((1/csc^2A)/(1/secA))-((1/sec^2A)/(1/cscA))`

`=(secA/csc^2A)-(cscA/sec^2A)=RHS`

Answer 2

See the answer below...

Explanation:

LHS
`=sin^2A/cosA-cos^2A/sinA`
`=sin^2A cdot 1/cosA-cos^2A cdot 1/sinA`
`=1/csc^2A cdot secA-1/sec^2A cdot cscA` `" "` `[color(red)(sintheta=1/csctheta" ; "costheta=1/sectheta)]`
`=secA/csc^2A-cscA/sec^2A`

Hope it helps...
Thank you...