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If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
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We have x = a `cos^3 theta `
= > `x/a = cos^3 theta ........(i)`
Again , `y = b sin^3 theta`
= > `y/b = sin^3 theta .....(ii)`
Now , LHS = `(x/a)^(2/3) + (y/b)^(2/3)`
= `( cos^3 theta )^(2/3) + (sin^3 theta )^ (2/3 )` [ from (i) and (ii)]
=` cos^2 theta + sin^2 theta `
=1
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