Question

How do you prove `tan(x/2)= sinx+cosxcotx-cotx`?

Answer 1

Develop the right side.

Explanation:

We know that `tan(x/2) = (1 - cos(x))/sin(x)`. So we develop the right side of the equality. `cot(x) = 1/tan(x)` so :

`sin(x) + cos(x)cot(x) - cot(x) = (sin^2(x) + cos^2(x) - cos(x))/sin(x) = (1-cos(x))/sin(x) = tan(x/2)`.