Question

If x = a cos³θ and y = b sin³θ, prove that `(x/a)^(2/3) + (y/b)^(2/3) = 1`.

Answer 1

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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