Question

If 5tan=4 then find the value of5sina-3cos /sin A+ 2 cos A

Answer 1

$Th e\: \: answer \: \: is \: \: given \: \: below \\ \\ Given \: \: that ,\: \: 5tanA = 4 \\ \\ So, \: \: tanA = \frac{4}{5} \\ \\ Now, \: \: \frac{5sinA - 3cosA}{sinA + 2cosA} \\ \\ Dividing \: \: both \: \: the \: \: numerator \\ and \: \: denominator \: \: by \: \: cosA, \: \: \\ we \: \: get \\ \\ \frac{5tanA - 3}{tanA+ 2} \: \: (Since, \: \: \frac{sinA}{cosA} = tanA )\\ \\ = \frac{5 \times \frac{4}{5} - 3}{ \frac{4}{5} + 2} \\ \\ = \frac{4 - 3}{ \frac{4 + 10}{5} } \\ \\ = \frac{1}{ \frac{14}{5} } \\ \\ = \frac{5}{14} \\ \\ Thank \: \: you \: \: for \: \: your \: \: question.$

Answer 2

Is my answer is true