Question

Tan^2/1-tan+cot/1-tan=cot+tan+1 prove that​

Answer 1

It looks like you have

tan²(x) / (1 - tan(x)) + cot(x) / (1 - tan(x)) = cot(x) + tan(x) + 1

but this is not an identity.

Take for instance x = 3π/4. Then

tan(3π/4) = -1

cot(3π/4) = -1

so that

tan²(x) / (1 - tan(x)) + cot(x) / (1 - tan(x)) = 0

while

cot(x) + tan(x) + 1 = -1

and of course 0 ≠ -1.