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(A) Let the angle be $	heta$. The angle is divided into two parts $\alpha$ and $\beta$ such that $	an \alpha = \frac{1}{2}$ and $	an \beta = \frac{

Vedclass · Accepted Answer

$\pi / 4$

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(A) Let the angle be $	heta$. The angle is divided into two parts $\alpha$ and $\beta$ such that $	an \alpha = \frac{1}{2}$ and $	an \beta = \frac{1}{3}$.Then, $	heta = \alpha + \beta = 	an^{-1}(\frac{1}{2}) + 	an^{-1}(\frac{1}{3})$.Using the formula $	an^{-1} x + 	an^{-1} y = 	an^{-1}(\frac{x+y}{1-xy})$ for $xy $	heta = 	an^{-1}\left(\frac{\frac{1}{2} + \frac{1}{3}}{1 - (\frac{1}{2} \cdot \frac{1}{3})}ight)$$	heta = 	an^{-1}\left(\frac{\frac{5}{6}}{1 - \frac{1}{6}}ight)$$	heta = 	an^{-1}\left(\frac{\frac{5}{6}}{\frac{5}{6}}ight)$$	heta = 	an^{-1}(1)$Since $	an(\frac{\pi}{4}) = 1$, we have $	heta = \frac{\pi}{4}$.

$A$ positive acute angle is divided into two parts whose tangents are $\frac{1}{2}$ and $\frac{1}{3}$. Then the angle is

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