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

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

AP EAMCETAP EAMCET 2020

Solution:

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