Question

simplify ${\tan }^{-1}\frac{3a^{2}x-x^3}{a(a^2-3x^2)}$

• A. $3{\tan }^{-1}\frac{x}{a}$
• B. ${\tan }^{-1}\frac{x}{a}$
• C. $3{\tan }^{-1}\frac{3x}{a}$
• D. ${\tan }^{-1}\frac{3x}{a}$

Answer 1

The correct option is A $3{\tan }^{-1}\frac{x}{a}$

Let $y={\tan }^{-1}\frac{3a^{2}x-x^3}{a(a^2-3x^2)}$
Put $x=a\tan \theta$
$\therefore y={\tan }^{-1}\frac{3\tan \theta -{\tan }^3\theta }{1-3{\tan }^2\theta }$
or $y={\tan }^{-1}\left(\tan 3\theta \right)=3\theta =3{\tan }^{-1}\frac{x}{a}$