$\sec^2{\theta}-\tan^2{\theta} \,=\, 1$

The subtraction of square of tan function from square of secant function equals to one is called the Pythagorean identity of secant and tangent functions.

In trigonometry, the secant and tangent are two functions, and they have a direct relation between them in square form but their relationship is derived from Pythagorean theorem. Therefore, the relation between secant and tangent functions in square form is called the Pythagorean identity of secant and tangent functions.

- $\Delta CAB$ is a right triangle and its angle is denoted by the symbol theta.
- The secant and tangent functions are written as $\sec{\theta}$ and $\tan{\theta}$ respectively.
- Similarly, their squares are written as $\sec^2{\theta}$ and $\tan^2{\theta}$ respectively in mathematical form.

The subtraction of the tan squared of angle from secant squared of angle is equal to one and it is called as the Pythagorean identity of secant and tangent functions.

$\sec^2{\theta}-\tan^2{\theta} \,=\, 1$

The Pythagorean identity of secant and tan functions can also be written popularly in two other forms.

- $\sec^2{x}-\tan^2{x} \,=\, 1$
- $\sec^2{A}-\tan^2{A} \,=\, 1$

Remember, the angle of a right triangle can be represented by any symbol but the relationship between secant and tan functions must be written in that symbol.

Learn how to prove the Pythagorean identity of secant and tan functions in mathematical form by geometrical method.

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Oct 22, 2024

Oct 17, 2024

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved