If 5 tan theta = 4,then frac{5 sin theta - 3 | vedclass

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Question

(C) Given $5 	an 	heta = 4$,which implies $	an 	heta = \frac{4}{5}$.To evaluate the expression $\frac{5 \sin 	heta - 3 \cos 	heta}{5 \sin 	heta

Vedclass · Accepted Answer

$1/6$

Vedclass · Answer

(C) Given $5 	an 	heta = 4$,which implies $	an 	heta = \frac{4}{5}$.To evaluate the expression $\frac{5 \sin 	heta - 3 \cos 	heta}{5 \sin 	heta + 2 \cos 	heta}$,divide both the numerator and the denominator by $\cos 	heta$:$= \frac{\frac{5 \sin 	heta}{\cos 	heta} - \frac{3 \cos 	heta}{\cos 	heta}}{\frac{5 \sin 	heta}{\cos 	heta} + \frac{2 \cos 	heta}{\cos 	heta}}$$= \frac{5 	an 	heta - 3}{5 	an 	heta + 2}$Substitute $	an 	heta = \frac{4}{5}$ into the expression:$= \frac{5(\frac{4}{5}) - 3}{5(\frac{4}{5}) + 2}$$= \frac{4 - 3}{4 + 2}$$= \frac{1}{6}$.

If $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta} = $

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