Math Doubts

Sec squared formula

Formula

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

The square of secant function equals to the addition of one and square of tan function is called the secant squared formula. It is also called as the square of secant function identity.

Introduction

The secant functions are sometimes involved in trigonometric expressions and equations in square form. The expressions and equations can be simplified by only transforming the secant squared functions into its equivalent form. Hence, it is must for learning the square of secant function identity for studying the advanced trigonometry further.

Usage

The secant squared trigonometric identity is sometimes used as a formula in two cases mostly.

  1. The square of secant function is expanded as the summation of one and the tangent squared function.
  2. The sum of one and the tan squared function is simplified as the square of secant function.

Popular forms

The secant squared function law is also expressed popularly in two forms in trigonometric mathematics.

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

Therefore, you can write the square of secant function formula in terms of any angle in this way in mathematics.

Proof

Let theta be a symbol, which represents an angle of a right triangle. The secant and tan functions are written as $\sec{\theta}$ and $\tan{\theta}$ respectively in mathematics. Mathematically, the relationship between secant and tan functions can be written in the following mathematical form according to the Pythagorean identity of secant and tan functions.

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

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

Therefore, it has derived successfully that the square of secant function is equal to the addition of one and square of tan function.

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