Answer to Question #144326 in Trigonometry for Shahir Sheikh

Question

Complete the Pythagorean Identity:

csc^2(x)−cot^2(x)=

Answer 1

Let us complete the Pythagorean Identity:

$\csc^2(x)−\cot^2(x)=(\frac{1}{\sin x})^2-(\frac{\cos x}{\sin x})^2=\frac{1}{\sin^2 x}-\frac{\cos^2 x}{\sin^2 x}=\frac{1-\cos^2 x}{\sin^2 x}=\frac{\sin^2 x}{\sin^2 x}=1.$