Question

If x = 4cosa and y = 5tana, find (x^2/16) - (y^2/25)​

Answer 1

$x = 4 \cos(a)$

$\frac{x}{4} = \cos(a)$

$( { \frac{x}{4} })^{2} = ({ \cos(a) })^{2}$

$\frac{ {x}^{2} }{16} = {cos}^{2} (a)$

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$y = 5 \tan(a)$

$\frac{y}{5} = \tan(a)$

$( { \frac{y}{5} })^{2} = ( { \tan(a) })^{2}$

$\frac{ {y}^{2} }{25} = {tan}^{2} (a)$

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Thus ;

$\frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{25} =$

${cos}^{2} (a) - {tan}^{2} (a)$