Prove the equation below is an identity

I think it's supposed to be "2sec^2x "  on the right side

(1+sin x)/(1 - sin x) =2sec^2x + 2sec x tan x - 1

Multiply top/bottom  on the left hand side by ( 1 + sinx)

[ 1 + sinx) (1 + sinx)] / [ (1 - sinx) (1 + sin x) ]  = 2sec^2x + 2sec x tan x - 1  

Simplify the LHS and remember that [ 1  = sec^2x - tan^2x]      

[ 1 + 2sinx + sin^2x] / (cos^2x]  =  2sec^2x  + 2secxtanx - [ sec^2x - tan^2x]

[ 1 + 2sinx + sin^2x] / (cos^2x]   = sec^2x + 2secxtanx + tan^2x

And, on the left, we can write :

1/cos^2x + [2sinx]/ [ cosx * cosx]  + [ sin^2x / cos^2x]

sec^2x  + 2[sinx/cosx] * [1/ cosx]  + tan^2x

sec^2x  + 2tanxsecx + tan^2x

sec^2x + 2secxtanx + tan^2x        and this equals the RHS

Yes! You're right about the problem being wrong! I couldn't figure out how to make something dquared using a keyboard and I didn't remember to state that! Thank you for your help!