Question

Prove that the equation is an identity.

sec x/(sec x -tan x)=sec^2 x +sec x tan x

Answer 1

left side

(1/cos) /(1/cos -sin/cos)

1/(1 - sin)

right side
1/cos^2 + sin/cos^2

(1+sin)/(1-sin^2)

(1+sin) / [(1+sin)(1-sin) ]

1/(1-sin) remarkable :)