Question #144326
Complete the Pythagorean Identity:

csc^2(x)−cot^2(x)=
1
Expert's answer
2020-11-22T14:03:50-0500

Let us complete the Pythagorean Identity:


csc2(x)cot2(x)=(1sinx)2(cosxsinx)2=1sin2xcos2xsin2x=1cos2xsin2x=sin2xsin2x=1.\csc^2(x)−\cot^2(x)=(\frac{1}{\sin x})^2-(\frac{\cos x}{\sin x})^2=\frac{1}{\sin^2 x}-\frac{\cos^2 x}{\sin^2 x}=\frac{1-\cos^2 x}{\sin^2 x}=\frac{\sin^2 x}{\sin^2 x}=1.



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