Question

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

Answer 1

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refer to the pic

Answer 2

Answer:

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5/14 is the required solution.

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Explanation:

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Given:

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5tanθ = 4

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To find:

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

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Solution:

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tanθ = sinθ/cosθ

tanθ = 4/5 , sinθ = 4 and cosθ = 5

by putting the above values here, we get

$\frac{5 \times 4 - 3 \times 5}{4 + 2 \times 5} \\ \\ = \frac{20 - 15}{14} = \frac{2}{14}$