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

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

The secant squared identity is used as a formula in two cases in trigonometry.

- The square of secant function is expanded as sum of one and tangent squared function.
- The sum of one and tan squared function is simplified as secant squared function.

The secant squared formula is actually derived from the Pythagorean identity of secant and tan functions.

If theta is angle of a right triangle, then the subtraction of squares of tan function from sec function equals to one.

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

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

Therefore, it is proved that secant squared theta is equal to the summation of one and tan squared theta.

The secant squared identity is also often written in terms of different angles.

For example, if $x$ is used to represent angle of right triangle, then the sec squared formula is written as $\sec^2{x} \,=\, 1+\tan^2{x}$

Hence, the angle of right angled triangle can be denoted by any symbol, the sec squared formula must be written in terms of the corresponding symbol.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.