If $ an^{- 1}2$ and $ an^{- 1}3$ are two angles of a triangle, then the third angle is

Question

If $	an^{- 1}2$ and $	an^{- 1}3$ are two angles of a triangle, then the third angle is

Dr. Abubacker · Accepted Answer

(c)
Given, two angles of triangle are $	an^{- 1}2$ and $	an^{- 1}3.$
Let third angle be $	heta$. Then,
$	an^{- 1}{2 + 	an^{- 1}{3 + 	heta = 180{^\circ}}}$
$\Rightarrow \ \ \ \ \ 	an^{- 1}{\left( \frac{2 + 3}{1 - 2 	imes 3} ight) = 180{^\circ} - 	heta}$
$\Rightarrow \ \ \ \ \frac{5}{- 5} = 	an{(180{^\circ} - 	heta) = - 	an	heta}$
$\Rightarrow \ \ \ \ \ \ 	an{	heta = 1 = 	an\frac{\pi}{4}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ 	heta = \frac{\pi}{4}$

Q. If $\tan^{- 1}2$ and $\tan^{- 1}3$ are two angles of a triangle, then the third angle is

Explanation

Reviewed by Dr. Abubacker

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