$ an^{-1}\left( frac{1}{2} ight) + an^{-1}\left( frac{1}{3} igh…

Question

$	an^{-1}\left(	frac{1}{2}ight) + 	an^{-1}\left(	frac{1}{3}ight)$ equals

Accepted Answer

C. $	frac{\pi}{4}$

Since $	frac{1}{2}\cdot	frac{1}{3} = 	frac{1}{6} < 1$, apply $	an^{-1}x + 	an^{-1}y = 	an^{-1}	frac{x+y}{1-xy}$.
Here $	frac{x+y}{1-xy} = 	frac{	frac{1}{2}+	frac{1}{3}}{1 - 	frac{1}{6}} = 	frac{5/6}{5/6} = 1$
so the sum is $	an^{-1}(1) = 	frac{\pi}{4}$.

Answer

$	frac{\pi}{2}$

Answer

$	frac{\pi}{3}$

Answer

$\pi$

$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ equals

Keep practising Unit 1A3: Function Composition and Inverses