Question

If x=a cos theta and y=b cot theta, show that (a²/x²)-(b²/y²)=1

Answer 1

Given,

x = a cos∅
So x = a² cos²∅

y = b cot ∅
So y² = b² cot²∅

Now,
$\frac{\cancel{{a}^{2}}}{\cancel{{a}^{2}} {cos}^{2}\varnothing}$ - $\frac{\cancel{{b}^{2}}}{\cancel{{b}^{2}} {cot}^{2}\varnothing}$
We know,
1/cos² = sec²
1/cot² = tan²

sec²∅ - tan²∅ = 1