How do you prove sec^2((pi/2)-x)-1=cot^2x?
1 Answer
Nov 21, 2015
We will be using the following properties:
sec(x) = 1/cos(x) (definition of secant)cot(x) = cos(x)/sin(x) (definition of cotangent)cos(-x) = cos(x) (cosine is even)cos(x - pi/2) = sin(x) sin^2(x) + cos^2(x) = 1
By 1, we have
By 3 and 4,
By 5,
Thus, by 2,
Substituting back then gives us