Question

tga=1/4 tg=(a-b)=2 tgb-?

Answer 1

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

$\frac{ \frac{1}{4} - \tan( \beta ) }{1 + \frac{1}{4} \times \tan( \beta ) } = 2$

$\frac{1}{4} - \tan( \beta ) = 2 \times \frac{1}{4} \tan( \beta ) + 2 \times 1 \\ \frac{1}{4} - 2 = \frac{1}{2} \tan( \beta ) + \tan( \beta ) \\ - 1 \frac{3}{4} = \frac{\tan( \beta ) + 2 \tan( \beta ) }{2} \\ - \frac{ 7}{4} \times 2 = 3 \tan( \beta ) \\ \frac{ - 7}{2} = \tan( \beta ) \\ \tan( \beta) = - 3.5$