If in a $\mathrm{\Delta}\ ABC,\angle A = an^{- 1}{2\ and\ \angle B = an^{- 1}{3,}}\$then angle $C$ is equal to

Question

If in a $\mathrm{\Delta}\ ABC,\angle A = 	an^{- 1}{2\ and\ \angle B = 	an^{- 1}{3,}}\$then angle $C$ is equal to

Dr. Abubacker · Accepted Answer

(c)
Given that, $\angle A = 	an^{- 1}{2,\angle B = 	an^{- 1}3}$
We know that, $\angle A + \angle B + \angle C = \pi$
$\Rightarrow 	an^{- 1}{2 + 	an^{- 1}{3 + \angle C = \pi}}$
$\Rightarrow 	an^{- 1}{\left( \frac{2 + 3}{1 - 2 	imes 3} ight) + \angle C = \pi}$
$\Rightarrow 	an^{- 1}{( - 1) + \angle C = \pi}$
$\Rightarrow \frac{3\pi}{4} + \angle C = \pi$
$\Rightarrow \angle C = \frac{\pi}{4}$

Q. If in a $\mathrm{\Delta}\ ABC,\angle A = \tan^{- 1}{2\ and\ \angle B = \tan^{- 1}{3,}}\$then angle $C$ is equal to

Explanation

Reviewed by Dr. Abubacker

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