Question

find the determinant of tanx

Answer 1

Derivative Proof of tan(x)



Derivative proof of tan(x)

We can prove this derivative by using the derivatives of sin and cos, as well as quotient rule.

Write tangent in terms of sine and cosine



Take the derivative of both sides



Use Quotient Rule





Simplify



Use the Pythagorean identity for sine and cosine



and simplify







Derivative proofs of csc(x), sec(x), and cot(x)

The derivative of these trig functions can be obtained easily from the Qoutient Rule using the reciprocals of sin(x), cos(x), and tan(x).