Question

If $\frac{sinA+cosA}{sinA-cosA}=\frac{5}{3},$ find the value of $\frac{7tanA+2}{2tanA+7}$

Answer 1

We have, $\frac{sinA+cosA}{sinA-cosA}=\frac{5}{3}\Rightarrow \frac{\frac{sinA}{cosA}+1}{\frac{sinA}{cosA}-1}=\frac{5}{3}$

$\Rightarrow \frac{tanA+1}{tanA-1}=\frac{5}{3}$

$\Rightarrow 3tanA+3=5tanA-5$

$\Rightarrow 2tanA=8$

$\Rightarrow tanA=4$

put $tanA=4$ in $\frac{7tanA+2}{2tanA+7}$

$\Rightarrow \frac{7tanA+2}{2tanA+7}=\frac{7\times 4+2}{2\times 4+7}$

$=\frac{28+2}{8+7}=\frac{30}{15}=2$