Question

$\text{If}\tan x=\frac{4}{5}.$ Then, find the value of
$\frac{5\sin x+3\cos x}{5\sin x-3\cos x}=$

• A. 7.0
• B. 7.00
• C. 7

Answer 1

Answer: (A), (B), (C)

Given: $\tan x=\frac{4}{5}$ and we have to find the value of the expression:

$\frac{5\sin x+3\cos x}{5\sin x-3\cos x}$

Dividing both numrerator and denominator by $\cos x$, we get
$\frac{5\frac{\sin x}{\cos x}+3\frac{\cos x}{\cos x}}{5\frac{\sin x}{\cos x}-3\frac{\cos x}{\cos x}}=\frac{5\tan x+3}{5\tan x-3}$

Since, $\tan x=4/3\Rightarrow \frac{5\tan x+3}{5\tan x-3}=\frac{5\times \frac{4}{5}+3}{5\times \frac{4}{5}-3}$
$\Rightarrow \frac{5\tan x+3}{5\tan x-3}=\frac{35}{5}=7$