Question

Please answer to my question

Answer 1

Answer:

$\tan( \alpha ) = \frac{5}{6} \\ \tan( \beta ) = \frac{1}{11} \\ \\ \tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } \\ = > \tan( \alpha + \beta ) = \frac{ \frac{5}{6} + \frac{1}{11} }{1 - ( \frac{5}{6} \times \frac{1}{11} )} \\ = > \tan( \alpha + \beta ) = \frac{ \frac{(5 \times 11) + (6 \times 1)}{6 \times 11} }{1 - \frac{5}{66} } \\ = > \tan( \alpha + \beta ) = \frac{ \frac{55 + 6}{66} }{ \frac{66 - 5}{66} } \\ = > \tan( \alpha + \beta ) = \frac{ \frac{61}{66} }{ \frac{61}{66} } \\ = > \tan( \alpha + \beta ) = 1 \\ = > \alpha + \beta = \tan^{ - 1} (1) \\ = > \alpha + \beta = \frac{\pi}{4}$