Question

How do you prove `2tan(x)sec(x) = (cos^2x+sin^2x)/(1-sin(x)) - (cos^2x+sin^2x)/(1+sin(x))`?

Answer 1

I changed all into `sin` and `cos`:

Explanation:

Try this:

Answer 2

Prove trig expression

Explanation:

Since `sin^2 x + cos^2 x = 1`, then,
`1/(1 - sin x) - 1/(1 + sin x) = [(1 + sin x) - (1 - sin x)]/(1 - sin^2 x) =`
`= (2sin x)/(cos^2 x) = ((2sin x)/cos x)(1/cos x) = 2tan x.(sec x)`