Question

In right triangle XYZ, the tangent of acute angle X is 4. What is the secant of angle X?

Answer 1

The secant of angle x; sec x = √17

Explanation:

Here, given the tangent of an angle, we want to find the value of the secant

Mathematically;

sec^2 x = 1 + tan^2 x

This is from trigonometric identity

Thus;

sec x = √(1 + tan^2 x)

According to the question;

tan x = 4

So tan^2 x = 4^2 = 16

Thus;

sec x = √1 + 4^2

sec x = √17