In addition to sine, cosine, and tangent, we have the trigonometric functions secant (sec), cosecant (csc), and cotangent (cot). We define these as follows:

for those values of x where the right side is defined. Explain why we must have cot^2 x + 1 = csc^2x for any x such that x is not an integer multiple of 180.

(Yes, I am aware this question was already posted, but I looked at CPhill's answer and didn't fully understand what he was doing. The thread was locked though, so I couldn't reply to his answer.)

Guest Mar 5, 2020

#1**+1 **

cot ^2 + 1 = 1/sin^2

cos^2/sin^2 + 1 = 1/sin^2 sub in sin^2 / sin^2 for 1

(cos^2 + sin^2)/sin^2 = 1/sin^2 see the numerator? Remember cos^2 + sin^2 = 1 ?

1/sin^2 = 1/sin^2 = csc^2

Can't have x as an integer multiple of 180 because sin is zero at those points and denominator 0 not defined.

ElectricPavlov Mar 5, 2020