Precalculus: proving trigonometric identity

[jessicagu93]

Homework Statement

prove that: tan(1+cos(x))^2 = 1-cos(x)

Homework Equations

trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc...

The Attempt at a Solution

i'm not sure where to start; i tried using the pythagorean identity where 1+tan(X)^2 = sec(x)^2, but couldn't get anywhere after that :\

then i used my calculator and made X a random number. i typed in the left side expression, and pressed enter. i then typed in the right hand expression, and pressed enter. the two values were different. what did i do wrong?
i'm not really sure anymore that its even possible to prove the above...

 

[Dick]

You're right. It's not an identity. Just put x=0. Then you don't even need a calculator. Must be some mistake here.

 

[snshusat161]

If I'm write you want to write $$tan(1 + cos x)^2$$ = 1 - cos(x). I think it is not possible to prove because if cos (x) is zero then $${tan}^2{1}$$ is not equal to 1. Even if the equation is $$tan(1 + {cos}^2{x})$$ then also you can't prove it. I think, the problem is not to prove but to solve.