Question

• A. 12/7
• B. 12/8
• C. 12/5
• D. 12/10

Answer 1

Answer:

A. 12/7

Given

$\tan\theta=4$

We know

$\tan\theta=\frac{\sin\theta}{\cos\theta}=4$

So, $\sin\theta=4\cos\theta$

Substitute this into the expression:

$\frac{4\cos\theta+2\sin\theta}{2\sin\theta-\cos\theta}$ $=\frac{4\cos\theta+2(4\cos\theta)} {2(4\cos\theta)-\cos\theta}$ $=\frac{4\cos\theta+8\cos\theta} {8\cos\theta-\cos\theta}$

$=\frac{12\cos\theta}{7\cos\theta}$

Therefore,

$=\boxed{\frac{12}{7}}$