Question

if 5 tan theta = 4 find the value of 5 sin theta - 3 cos theta/5 sin theta + 3 cos theta

Answer 1

Answer:

if 5 tan theta = 4 find the value of 5 sin theta - 3 cos theta/5 sin theta + 3 cos theta

Answer 2

Answer:

1/7

Step-by-step explanation:

Given,

5 tan theta = 4

tan theta = 4/5

Sin Theta/Cos Theta = 4/5

Let the sides be x.

Sin Theta = 4x

Cos Theta = 5x

$\dfrac{5 \sin\theta - 3 \cos\theta}{5 \sin\theta + 3 \cos\theta}$

5 Sin Theta = 20x

3 Cos Theta = 15x

$\dfrac{20x - 15x}{20x + 15x} \\ \\ \dfrac{5x}{35x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dfrac{1}{7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$