Question

If tan alpha is equals to 1 by 2 and 10 theta is equals to 1 by 3 then alpha + beta is equals to

Answer 1

Step-by-step explanation:

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Answer 2

Given :

$\tan \alpha = \frac{1}{2}\\\\\tan \beta = \frac{1}{3}$

To find: $(\alpha + \beta)$

Solution :

$\tan \alpha = \dfrac{1}{2}\\\\\tan \beta = \dfrac{1}{3}\\\\\tan (\alpha + \beta)= \dfrac{\tan \alpha+\tan \beta}{1- \tan \alpha \times \tan \beta}\\\\= \dfrac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\times \frac{1}{3} }\\\\=\dfrac{\frac{5}{6}}{1-\frac{1}{6}}\\\\= \dfrac{\frac{5}{6}}{\frac{5}{6}}= 1\\\\\tan (\alpha + \beta)=1\\\\(\alpha + \beta)= \tan^{-1} (1)\\\\(\alpha + \beta)=\dfrac{\pi}{4}$

Hence , The value of $(\alpha + \beta)=\frac{\pi}{4}$.