Differentiation Question 411

Question: If $ x=a{{\cos }^{3}}\theta ,y=a{{\sin }^{3}}\theta $ , then $ \sqrt{1+{{( \frac{dy}{dx} )}^{2}}}= $

[EAMCET 1992]

Options:

A) $ {{\tan }^{2}}\theta $

B) $ {{\sec }^{2}}\theta $

C) $ \sec \theta $

D) $ |\sec \theta | $

Show Answer

Answer:

Correct Answer: D

Solution:

$ \sqrt{1+{{\tan }^{2}}\theta }=|\sec \theta | $ .