In this video I go over the proof of the trigonometry identity tan²(x) + 1 = sec²(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: sin²(x) + cos²(x) = 1 (the proof of this identity is shown my earlier videos). The derivation of identity is to simply divide the Pythagorean trig identity by cos²(x) on both sides and use the definitions of tan(x) and sec(x) to re-write the resulting identity.

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Trigonometry Identity: tan²(x) + 1 = sec²(x)

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

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Trigonometry Identity: tan2(x) + 1 = sec2(x)

Trigonometry Identity: tan²(x) + 1 = sec²(x)