Question

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

Answer 1

`x = 4 \cos(a)`

`(x)/(4) = \cos(a) \\`

`( { (x)/(4) })^(2) = ({ \cos(a) })^(2) \\`

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

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`y = 5 \tan(a)`

`(y)/(5) = \tan(a) \\`

`( { (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)`