Question

if tan(theta) = 3/4, find the value of 4 sin Q - cos Q/ 4sin Q + 4 cos Q​

Answer 1

Answer:

The answer is $\dfrac{2}{7}$

Step-by-step explanation:

Given  $\tan \theta=\dfrac{3}{4}$

Thus

      $\dfrac{4\sin\theta-\cos\theta}{4\sin\theta+4\cos\theta}=\dfrac{4(\frac{\sin\theta}{\cos\theta})-1}{4(\frac{\sin\theta}{\cos\theta})+4}$ , divide numerator and denominator by $\cos\theta$

       $=\dfrac{4\tan\theta-1}{4\tan\theta+4}=\dfrac{4(3/4)-1}{4(3/4)+4}=\dfrac{3-1}{3+4}=\dfrac{2}{7}$