Pythagorean

Pythagorean identity with tangent: 1 + tan²θ = sec²θ

1+tan2θ=sec2θ1 + \tan^{2}\theta = \sec^{2}\theta

Dividing sin²θ + cos²θ = 1 through by cos²θ gives 1 + tan²θ = sec²θ. Reach for it whenever an expression mixes tangents and secants - it is the substitution behind the trigonometric-substitution integral for √(x² + a²).

Related Pythagorean identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Pythagorean questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.