Pythagorean Identities

Theorem

Sum of Squares of Sine and Cosine

$\cos^2 x + \sin^2 x = 1$


Difference of Squares of Secant and Tangent

$\sec^2 x - \tan^2 x = 1 \quad \text {(when $\cos x \ne 0$)}$


Difference of Squares of Cosecant and Cotangent

$\csc^2 x - \cot^2 x = 1 \quad \text {(when $\sin x \ne 0$)}$


Source of Name

This entry was named for Pythagoras of Samos.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Pythagorean identities
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pythagorean identities
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function
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