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Question

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

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Solution

(sec θtan θ)x+(sec θ+tan θ)y=2

x2(sin θtan θ)+y2(sec θ+tan θ)=1

So,a=2sec θtan θ,b=2sec θ+tan θ

Area of required triangle

A=12ab

=12(2sec θtan θ)(2sec θ+tan θ)

=2sec2θtan2θ

A=2 sq,units


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