Question

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

Collected in the board: Trigonometry

Steven Zheng posted 2 months ago


Answer

Apply sum identity for tangent function,

\tan(\alpha+\beta) = \dfrac{\tan \alpha + \tan \beta }{1-\tan \alpha\tan \beta}

= \dfrac{2+3}{1-2\times 3 } = -1

Since \alpha and \beta are acute angles

0< \alpha+\beta < \pi

Therefore,

\alpha +\beta =\dfrac{3\pi}{4}

Steven Zheng posted 2 months ago

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