Question

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

Answer 1

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

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

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