If x = cos3θ, y = bsin3θ,prove that\(\Big(\frac{x}{a}\Big)^{2/3}+\Bi

1.	If x = cos3θ, y = bsin3θ,prove that\(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}=1\)
Answer» x = acos³θ ⇒ \(\frac{x}{a}\) = cos³θ y = bsin³θ ⇒ \(\frac{y}{b}\) = sin³θ Now, \(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}\) = (cos³θ)^2/3 + (sin³θ)^2/3 = cos²θ +sin²θ = 1 \(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}\) = 1

If x = cos3θ, y = bsin3θ,prove that\(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}=1\)

Answer»

x = acos³θ ⇒ \(\frac{x}{a}\) = cos³θ

y = bsin³θ ⇒ \(\frac{y}{b}\) = sin³θ

Now, \(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}\) = (cos³θ)^2/3 + (sin³θ)^2/3

= cos²θ +sin²θ

= 1

\(\Big(\frac{x}{a}\Big)^{2/3}+\Big(\frac{y}{b}\Big)^{2/3}\) = 1