Question

The area (in sq. units) of the triangle formed by the coordinate axes and the line $x\left(\tan \theta \right)+y\left(\cot \theta \right)=4$ where $\theta \in (0,\frac{\pi }{2}),$ is

Answer 1

Given line is $x\left(\tan \theta \right)+y\left(\cot \theta \right)=4$
$\Rightarrow \frac{x}{4\cot \theta }+\frac{y}{4\tan \theta }=1$

So, the area formed by the line and the coordinate axes
$=\frac{1}{2}\times |4\cot \theta \times 4\tan \theta |=8$