Question

Simplify ${\tan }^{-1}\frac{5ax}{a^2-6x^2}$

• A. ${\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{2x}{a}$
• B. ${\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{-2x}{a}$
• C. ${\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{x}{a}$
• D. ${\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{-x}{a}$

Answer 1

The correct option is A ${\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{2x}{a}$

Let $y={\tan }^{-1}\frac{5ax}{a^2-6x^2}$

$={\tan }^{-1}\frac{3ax+2ax}{a^2-6x^2}$

Divide by $a^2.$
$y={\tan }^{-1}\frac{\frac{3x}{a}+\frac{2x}{a}}{1-\frac{3x}{a}\cdot \frac{2x}{a}}$

$={\tan }^{-1}\frac{3x}{a}+{\tan }^{-1}\frac{2x}{a}$