Question

if 3 tan Q=4 find the value of 5sinQ-3cosQ/5sinQ+2cosQ

Answer 1

$\sf Given: 3\ tanQ\ =\ 4.\\\\To\ find: The\ value\ of\ \frac{5\ sinQ\ -\ 3\ cosQ}{5\ sinQ\ +\ 2\ cosQ}\\\\Answer:\\\\3\ tanQ\ =\ 4\\\\tanQ\ = \frac{4}{3} \\\\Dividing\ both\ the\ numerator\ and\ denominator\ of\  \frac{5\ sinQ\ -\ 3\ cosQ}{5\ sinQ\ +\ 2\ cosQ}\ by\ sinQ, \\\\\frac{\frac{5\ sinQ\ -\ 3\ cosQ}{sinQ} }{\frac{5\ sinQ\ +\ 2\ cosQ}{sinQ}}\\\\We\ get\ \frac{5\ -\ 3\ tanQ}{5\ +\ 2\ tanQ}.\\\\Substituting\ the\ value\ of\ tanQ\ in\ the\ above\ fraction,$$\sf \frac{5\ -\ 3(\frac{4}{3})}{5\ +\ 2 (\frac{4}{3})} \\\\= \frac{5\ -\ 4}{5\ +\ \frac{8}{3}} \\\\= \frac{1}{\frac{15\ +\ 8}{3}} \\\\= \frac{3}{15\ +\ 8} \\\\= \frac{3}{23} \\\\Therefore, \frac{5\ sinQ\ -\ 3\ cosQ}{5\ sinQ\ +\ 2\ cosQ} = \frac{3}{23}$

Answer 2

it's the upper one, No need to thank me