Write the area of the triangle formed by the coordinate axes and the line `(s e ctheta-t a ntheta)x+(s e ctheta+t a ntheta)y=2.`

Explanation

The point of intersection of the coordinate axes is (0, 0)

.Let us find the intersection of the line `(secθ − tan θ) x + (sec θ + tan θ) y = 2 `and the coordinate axis.

For x-axis: `y = 0, x = 2(secθ−tanθ)`

For y-axis:` x = 0, y = 2/secθ−tanθ)`

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),(2/(secθ−tanθ),0),(0,2/(secθ−tanθ))`

So area of traingle is

=`1/2[[0,0,1],[2/(secθ−tanθ),0,1],[0,2/(secθ+tanθ)
,1]]`

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