Question

If $x=a{\cos }^3\theta$ and y = b ${\sin }^3\theta ,$ then the value of ${\left(\frac{x}{a}\right)}^{2/3}+{\left(\frac{y}{b}\right)}^{2/3}$ is

• A. 1
• B. -2
• C. 2
• D. -1

Answer 1

The correct option is A 1

The value of ${\left(\frac{x}{a}\right)}^{\frac{2}{3}}+{\left(\frac{y}{b}\right)}^{\frac{2}{3}}$ is

$={\left(3\sqrt{\frac{a{\cos }^3\theta }{a}}\right)}^2+{\left(3\sqrt{\frac{b{\sin }^3\theta }{b}}\right)}^2$

$={\left(\sin \theta \right)}^2+{\left(\cos \theta \right)}^2={\sin }^2\theta +{\cos }^2\theta =1$