 # Sec 90

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 in this way, 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 arc in starting. The inverse name of sec is arcsec.

The value of Secant 90 degree cannot be calculated and is undefined in the trigonometric table. ## How to calculate Sec 90?

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/cosx

Sec 90 = 1/ cos 90

Sec 90 = 1/ 0

Sec 90 = undefined

## Examples on Sec 90 Value:

Question 1: What is the value of Sec(270 – x) Sec(90 – x) – tan (270 – x) tan (90 – x)?

Solution: Sec(270 – x) Sec(90 – x) – tan (270 – x) tan (90 – x)?

=( – cosec x cosec x) – ( – cot x cot x)

= -cosec 2 x + cot2 x

= – 1

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