Question

If
$\alpha + \beta = \pi \div 4$then prove that
$\tan\alpha + \tan \beta + \tan \alpha \tan \beta = 1$
​

Answer 1

Answer:

$\tan( \alpha + \beta ) = \tan( \frac{\pi}{4} )$

$\frac{ \tan( \alpha) + \tan( \beta ) }{1 - \tan( \alpha ) \times \tan( \beta ) } = 1$

$\tan( \alpha ) + \tan( \beta ) = 1 - \tan( \alpha ) \tan( \beta )$

$\tan( \alpha ) + \tan( \beta ) + \tan( \alpha ) \tan( \beta ) = 1$