SOLUTION: In addition to sine, cosine, and tangent, we have the trigonometric functions secant (sec), cosecant (csc), and cotangent (cot). We define these as follows: sec x =1/{cos x} cs

Question 1079090: In addition to sine, cosine, and tangent, we have the trigonometric functions secant (sec), cosecant (csc), and cotangent (cot). We define these as follows:
sec x =1/{cos x}
csc x =1/{sin x},
cot x = {cos x}/{sin x},
for those values of x where the right side is defined.
Explain why we must have (cot^2)x + 1 = (csc^2)x for any x such that x is not an integer multiple of 180 degrees.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Explain why we must have (cot^2)x + 1 = (csc^2)x for any x such that x is not an integer multiple of 180 degrees.
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I can prove it's true, not sure "why we must have it..."
(cot^2)x + 1 = (csc^2)x
cos^2/sin^2 + 1 = 1/sin^2
Multiply by sin^2
cos^2 + sin^2 = 1 --- the Pythagorean Identity.

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