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If 5 tan $A = 4$ , evaluate $\frac{5 s i n A - 3 c o s A}{5 s i n A + 2 c o s A}$ .

Class 10Trigonometric IdentitiesTrigonometry

A $\frac{1}{6}$
B $\frac{5}{6}$
C $\frac{1}{2}$
D $\frac{2}{3}$

Step-by-Step Solution

tan

A = \frac{4}{5}

. Divide num and denom by cos A:

\frac{5 t a n A - 3}{5 t a n A + 2} = \frac{5 \cdot \frac{4}{5} - 3}{5 \cdot \frac{4}{5} + 2} = \frac{4 - 3}{4 + 2} = \frac{1}{6}

.

Answer: A)

\frac{1}{6}

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