Question

if 3 tanθ =4, find the value of 4cosθ-sinθ/ 2cosθ+sinθ

Answer 1

$3 \tan( \alpha ) = 4 \\ \\ \tan( \alpha ) = \frac{4}{3} \\ \\ y = \frac{4 \cos( \alpha ) - \sin( \alpha ) }{2 \cos( \alpha ) + \sin( \alpha ) } \\ \\ Dividing \: \: numerator \: \: and \: \: \\ denominator \: by \: \cos( \alpha ) \: , \\ \\ y = \: \frac{ 4 - \tan( \alpha ) }{2 + \tan( \alpha ) } \\ \\ y = \frac{4 - \frac{4}{3} }{2 + \frac{4}{3} } \\ \\ \\ \large \boxed { \color{Purple}{y = \frac{8}{10} = \bf \frac{4}{5} }}$