, if k is an odd integer,

, if k is an even integer.

Here T can be any trigonometric functions, and co-T is the co-function of function T. For example, sine and cosine are co-functions of each other, similarly tangent and cotangent, secant and cosecant respectively.

For example

and so on, all of such formulas can proved by the Sum and Difference formulas:

,

since     .

since     , and so on.  In the same way we can prove all of them.