If $$\alpha$$ and $$\beta$$ are acute angles such that $$ an \alpha =2$$, $$ an \beta =3$$, verify $$\alpha +\beta =\dfrac{3\pi}{4} $$

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If  $$\alpha$$ and $$\beta$$ are acute angles such that $$ 	an \alpha =2$$, $$	an \beta =3$$,   verify $$\alpha +\beta =\dfrac{3\pi}{4} $$

Uniteasy Admin · Accepted Answer

Apply sum identity for tangent function,
$$	an(\alpha+\beta) = \dfrac{	an \alpha + 	an \beta }{1-	an \alpha	an \beta}$$
$$= \dfrac{2+3}{1-2	imes 3 } = -1 $$
Since $$\alpha$$ and $$\beta$$ are acute angles
$$ 0< \alpha+\beta < \pi$$
Therefore,
$$\alpha +\beta =\dfrac{3\pi}{4} $$

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