Given:

Line (sec θ – tan θ)x + (sec θ + tan θ) y = 2.

To find:

The area of the triangle formed by the coordinate axes and the line (sec θ – tan θ)x + (sec θ + tan θ) y = 2.

Explanation:

The point of intersection of the coordinate axes is (0, 0).
Let us find the intersection of the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2 and the coordinate axis.

For x-axis:

y = 0, x

For y-axis:

x = 0, y

Thus, the coordinates of the triangle formed by the coordinate axis and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2 are (0, 0), and .

Let A be the area of the required triangle.

∴ A

⇒ A

⇒ A

Hence, the area of the triangle is 2 square units.