Question

If $4\cos x+3\sin x=5$,then find the value of $\tan x=$

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{-3}{4}$
• D. $\frac{-4}{3}$

Answer 1

Answer: (A)

Given, $4\cos x+3\sin x=5$
$\Rightarrow 4+3\tan x=5\sec x$
On squaring both sides, we get
$16+9{\tan }^{2}x+24\tan x=25{\sec }^{2}x$
$\Rightarrow (4\tan x-3{)}^2=0$
$\Rightarrow \tan x=\frac{3}{4}$