Cosine squared theta = 1 + Sine squared theta
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There is no easy simplification.
The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
An even function is one where f(x) = f(-x) For cosine, cos(x) = cos(-x), thus cosine is an even function.
The inverse (negatives) of sine, cosine, and tangent are used to calculate the angle theta (or whatever you choose to name it). Initially it is taught that opposite over hypotenuse is equal to the sine of theta sin(theta) = opposite/hypotenuse So it can be said that theta = sin-1 (opp/hyp) This works the same way with cosine and tangent In short the inverse is simply what you use when you move the sin, cos, or tan to the other side of the equation generally to find the angle
1 - sin2(q) = cos2(q)dividing through by cos2(q),sec2(q) - tan2(q) = 1