Question

If Tan theta= 3/4
evaluate 4Sin theta- Cos theta / 4Sin theta + Cos theta​

Answer 1

Answer:

The answer is $\frac{1}{2}$

Step-by-step explanation:

Given  $\tan\theta=\frac{3}{4}$

Therefore    

              $\displaystyle \frac{4\sin\theta-\cos\theta}{4\sin\theta+\cos\theta}$

             $=\displaystyle \frac{\frac{4\sin\theta-\cos\theta}{\cos\theta}}{\frac{4\sin\theta+\cos\theta}{\cos\theta}}\\ =\frac{4\times \frac{\sin\theta}{\cos\theta}-\frac{\cos\theta}{\cos\theta}}{4\times \frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\cos\theta}}\\=\frac{4\tan\theta-1}{4\tan\theta+1}\\=\frac{4\times \frac{3}{4}-1}{4\times \frac{3}{4}+1}\\=\frac{3-1}{3+1}=\frac{2}{4}=\frac{1}{2}$