Question

Let $x=a\cos ({90}^o-\theta )$ and $y=b\cot ({90}^o-\theta )$ then prove that $\frac{a^2}{x^2}-\frac{b^2}{y^2}=1$.

Answer 1

Given, $x=a\cos ({90}^o-\theta )$ and $y=b\cot ({90}^o-\theta )$

or, $x=a\sin \theta$ and $y=b\tan \theta$

or, $\frac{a}{x}=cosec\theta$ and $\frac{b}{y}=\cot \theta$.

Now,

$\frac{a^2}{x^2}-\frac{b^2}{y^2}$

$=cose{c}^2\theta -{\cot }^2\theta$

$=1$.