Trigonometry Identity: tan^2(x) + 1 = sec^2(x)

In this video I go over the proof of the trigonometry identity tan^2(x) + 1 = sec^2(x). The proof of this identity is very simple and like many other trig identities, stems from the basic trig identity, known as the Pythagorean trig identity: sin^2(x) + cos^2(x) = 1 (the proof of this identity is shown in the related videos below). The derivation of identity is to simply divide the Pythagorean trig identity by cos^2(x) on both sides and use the definitions of tan(x) and sec(x) to re-write the resulting identity.

Related Videos:

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I don't always derive trigonometry identities but when I do I usually use a more basic identity to prove it ;)