Tangent and cotangent/Monotonicity behavior/Fact/Proof/Exercise
Show that the real tangent function induces a bijective, strictly increasing function
and that the real cotangent function induces a bijective strictly decreasing function
Show that the real tangent function induces a bijective, strictly increasing function
![{\displaystyle ]-\pi /2,\pi /2[\longrightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1baa86bbe684c91bd8b91ba9bd4519ebcf18a3d5)
and that the real cotangent function induces a bijective strictly decreasing function
![{\displaystyle [0,\pi ]\longrightarrow \mathbb {R} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/014d0207862d72a4533c62948f6bae80d18e9964)