Question

If 5 tan a = 4, prove that
5 sin a - 2 cos a/5 sin a + 3 cos a=1/6​

Answer 1

Answer:

$\red {Value \:of \: \frac{5sinA -2cosA}{5sinA + 3cosA}}\green {= \frac{2}{7}}$

Step-by-step explanation:

$Given \: 5tan A = 4 \\\implies \frac{5sinA}{cosA} = 4 \\\implies 5sinA = 4cosA \: --(1)$

$Value \:of \: \frac{5sinA -2cosA}{5sinA + 3cosA}\\= \frac{4cosA - 2cosA}{4cosA + 3cosA}\: [ From \:(1)]$

$= \frac{2cosA}{7cosA}\\= \frac{2}{7}$

Therefore.,

$\red {Value \:of \: \frac{5sinA -2cosA}{5sinA + 3cosA}}\green {= \frac{2}{7}}$

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