Question

Prove `(secX-tanX)/(secX+tanX) = 1-2secXtanX+2tan^2X`?

Answer 1

`LHS=(secX-tanX)/(secX+tanX)`

`=(secX-tanX)^2/((secX+tanX)(secX-tanX))`

`=(sec^2X+tan^2X-2secXtanX)/(sec^2X-tan^2X)`
`=(1+tan^2X+tan^2X-2secXtanX)/(1+tan^2X-tan^2X)`

`= 1-2secXtanX+2tan^2X=RHS`