Eliminate-if-x-a-sec-3-and-y-b-tan-3-

Question Number 6872 by hanandmishra026@gmail.com last updated on 31/Jul/16

E l i m i n a t e θ i f x = a \sec^{3} θ a n d y = b \tan^{3} θ

Commented by Yozzii last updated on 31/Jul/16

s e c θ = {(\frac{x}{a})}^{1 / 3}, t a n θ = {(\frac{y}{b})}^{1 / 3}

{s e c}^{2} θ = 1 + {t a n}^{2} θ

\Rightarrow {(\frac{x}{a})}^{2 / 3} = 1 + {(\frac{y}{b})}^{2 / 3}

{(b x)}^{2 / 3} = {(a b)}^{2 / 3} + {(a y)}^{2 / 3}

{(b x)}^{2 / 3} - {(a y)}^{2 / 3} = {(a b)}^{2 / 3}

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