Question

If x=a `cos^3 theta and y = b sin ^3 theta ," 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

𝐻𝑒𝑛𝑐𝑒, 𝐿𝐻𝑆 = 𝑅𝐻𝑆