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- The antiderivative of 0 is a constant
- Series definition of sine and cosine (in particular and )
- Differential of is , differential of is
- Linearity of the derivative, the Chain rule
(linearity of the derivative)
(evaluating the differentials)
As the derivative of the expression is zero, this implies for some constant k. Evaluating at , which means , implying
It is possible to use geometry to prove the statement, however it only holds for
- Pythagorean Theorem: , in any right triangle. - [ Proof ]
- The definition of the trigonometric functions as ratios of the sides of a right triangle:
Given an arbitrary right triangle, the following are true:
Via the Pythagorean Theorem, the legs (here: opposite and adjacent) are "a," and "b" where hypotenuse is "c".