Question

if 4 tan A is equal to 3 the value of 2 Sin A + Cos A divided by 3 sin a - 2 cos A is what​

Answer 1

Answer:

14

Step-by-step explanation:

tan A =$\frac{3}{4}$=$\frac{P}{B}$

Therefore P=3k and B=4k

H²=P²+B²

H²=(3k)²+(4k)²

H²=9k²+16k²

H²=25k²

H=5k

Sin A =$\frac{P}{H}$=$\frac{3}{5}$

Cos A=$\frac{B}{H}$=$\frac{4}{5}$

2 Sin A + cos A=2×$\frac{3}{5}$+$\frac{4}{5}$

=$\frac{10+4}{5}$

=$\frac{14}{5}$

3 Sin A -2 cos A=3×$\frac{3}{5}$-2×$\frac{4}{5}$

=$\frac{9-8}{5}$

=$\frac{1}{5}$

$\frac{2 Sin A + Cos A}{3 SinA - 2 Cos A}$=$\frac{14}{5}$÷$\frac{1}{5}$

=$\frac{14}{5}$×$\frac{5}{1}$

=14