Answer :

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.


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