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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.)

 Mar 5, 2020
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cot ^2   + 1   =    1/sin^2

cos^2/sin^2  + = 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.

 Mar 5, 2020
edited by ElectricPavlov  Mar 5, 2020
edited by ElectricPavlov  Mar 6, 2020

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