Deriving the Secondary Pythagorean Trig Identities

This video uses the Pythagorean Identity \(\sin^2 x+\cos^2 x=1\) to derive the secondary Pythagorean Identities \(1+\tan^2 x=\sec^2 x\) and \(1+\cot^2 x = \csc^2 x.\) The key to deriving the formulas is to divide both sides of the identity by either \(\sin^2 x\) or \(\cos^2 x\) and then use the reciprocal and ratio identities.