$ an^{-1}(1) + an^{-1}(2) + an^{-1}(3) = $

Question

$	an^{-1}(1) + 	an^{-1}(2) + 	an^{-1}(3) = $

Accepted Answer

D. $\pi$

For $	an^{-1}(2) + 	an^{-1}(3)$, the product $2\cdot 3 = 6 > 1$
so use $	an^{-1}x + 	an^{-1}y = \pi + 	an^{-1}	frac{x+y}{1-xy}$ (positive case).
This gives $\pi + 	an^{-1}	frac{5}{-5} = \pi + 	an^{-1}(-1) = \pi - 	frac{\pi}{4} = 	frac{3\pi}{4}$.
Adding $	an^{-1}(1) = 	frac{\pi}{4}$: total $= \pi$.

Answer

$	frac{\pi}{2}$

Answer

$	frac{5\pi}{4}$

Answer

$	frac{3\pi}{4}$

$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $

Keep practising Unit 1A3: Function Composition and Inverses