Question

Show that {sec^(4)x-1}/{tan^(2)x}={tan^(2)x+2}?

Answer 1

`LHS={sec^(4)x-1}/{tan^(2)x}`

`={(1+tan^2x)^2-1}/{tan^(2)x}`

`=(1+2tan^2x+tan^4x-1}/{tan^(2)x}`
`=(2tan^2x+tan^4x}/{tan^(2)x}`

`=tan^(2)x+2=RHS`