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Relation between Trigonometric Ratios

If 5cos A =...

Question

If $5 cos A = 4 sin A$ , then $tan A =___$

\frac{1}{4}

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\frac{5}{4}

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5

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\frac{4}{5}

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Solution

The correct option is B $\frac{5}{4}$
$5 cos A = 4 sin A$
$\Rightarrow \frac{5 cos A}{4 cos A} = \frac{4 sin A}{4 cos A}$ by dividing both sides by $4 sin A$
$\Rightarrow \frac{sin A}{cos A} = \frac{5}{4}$
$∴ tan A = \frac{5}{4}$

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\frac{4 s i n A - 3 c o s A}{t a n A} .

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