If 4 cos x + 3 sin x = 5,then find the value | vedclass

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Question

(A) Given,$4 \cos x + 3 \sin x = 5$. Divide both sides by $\cos x$ (assuming $\cos x 
eq 0$): $4 + 3 	an x = 5 \sec x$. Squaring both sides: $(4 + 3

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) Given,$4 \cos x + 3 \sin x = 5$. Divide both sides by $\cos x$ (assuming $\cos x 
eq 0$): $4 + 3 	an x = 5 \sec x$. Squaring both sides: $(4 + 3 	an x)^2 = (5 \sec x)^2$. $16 + 9 	an^2 x + 24 	an x = 25 \sec^2 x$. Using the identity $\sec^2 x = 1 + 	an^2 x$: $16 + 9 	an^2 x + 24 	an x = 25(1 + 	an^2 x)$. $16 + 9 	an^2 x + 24 	an x = 25 + 25 	an^2 x$. Rearranging the terms: $16 	an^2 x - 24 	an x + 9 = 0$. $(4 	an x - 3)^2 = 0$. Therefore,$4 	an x = 3$,which gives $	an x = \frac{3}{4}$.

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

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