Question

If 3 cot theta =4 find 5cos theta -2sin theta / 5 cos theta +3 sin theta

Answer 1

$Given \: 3 cot \theta = 4\\ \implies cot \theta = \frac{4}{3} \: ---(1)$

$Now, Value \: of \: \frac{5 cos \theta - 2sin \theta }{ 5cos \theta + 3 sin \theta }$

$Dividing\: numerator \:and\: denominator \:\\by \: sin \theta , \:we \: get$

$= \frac{\frac{5 cos \theta - 2sin \theta }{sin \theta}}{\frac{ 5cos \theta + 3 sin \theta}{sin \theta} }$

$= \frac{ \frac{5cos\theta}{sin\theta} + \frac{2sin\theta}{sin\theta}}{\frac{5cos \theta}{sin\theta} + \frac{3sin \theta}{sin\theta}}$

$= \frac{5cot \theta - 2 }{5 cot \theta + 3} \\= \frac{5 \times \frac{4}{3} - 2}{ 5 \times \frac{4}{3} + 3} \: [From \: (1 )] \\= \frac{\frac{20}{3} - 2}{\frac{20}{3} + 3 } \\= \frac{\frac{20-6}{3}}{ \frac{20+9}{3}} \\= \frac{14}{3} \times \frac{3}{29} \\= \frac{14}{29}$

Therefore.,

$\red { Value \: of \: \frac{5 cos \theta - 2sin \theta }{ 5cos \theta + 3 sin \theta } }\green {= \frac{14}{29}}$

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Answer 2

Hope this helps. Drop in a thanks. Mark as brainliest