# Sec 0

The sec of an angle in a right triangle is the ratio of the length of the hypotenuse to the length of the adjacent side.

In triangle PQR right-angled at Q, sec x = Hypotenuse / Adjacent side

Secant can be easily replaced by cos x using the formula, **sec x = 1 / cos x.**

## The inverse sec x formula –

For every trigonometric function, there is always an inverse function that works in reverse. These all inverse functions have the name as the arc in starting. The inverse name of sec is arcsec.

The value of Secant 90 degree cannot be calculated and is undefined, i.e. infinity in the trigonometric table.

## How to calculate Sec 0?

As the angle is between 0 and 90 degrees, it is located in 1st quadrant, where the value of sin, cos and tan are positive. 90 degrees is always a right angle.

sec x = 1/cos x

sec 0 = 1/ cos 0

sec 0 = 1/ 1

sec 0 = 1

**Question on Sec x**

**Question: **What is the value of tan x, if sec x is 1?

**Answer: **

sec^{2 } x = 1 + tan ^{2 }x

sec^{2 } x – 1 = tan ^{2 }x

(1)^{2} – 1 = tan ^{2 }x

(1)^{2} – 1 = tan ^{2 }x

1 – 1 = tan ^{2}x

tan x = 0

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