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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\(^\circ \).

 Mar 16, 2019
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cot^2 x  =   cos^2 x / sin^2 x

And 1   =  sin^2x / sin^2 x

 

So

 

cot^2 x  + 1   =

 

cos^2 x / sin^2 x    +  sin^2 x / sin^2x  =

 

[ cos^2 x + sin ^2 x ]  / sin^2 x  =

 

1 / sin^2x  =

 

(1 / sin x)^2  =

 

csc^2 x

 

 

cool cool cool

 Mar 16, 2019

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