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

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Aicharya · Accepted Answer

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

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

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