Question

If $\frac{\cos x}{a} = \frac{\cos(x + \theta)}{b} = \frac{\cos(x + 2\theta)}{c} = \frac{\cos(x + 3\theta)}{d}$ then $\frac{a + c}{b + d}$is equal to

• A. $\frac{a}{d}$
• B. $\frac{c}{d}$
• C. $\frac{b}{c}$
• D. $\frac{d}{a}$

Answer 1

Answer: (C)

$\frac{b}{c}$

Answer 2

$\frac{a + c}{b + d} = \frac{\cos x + \cos(x + 2\theta)}{\cos(x + \theta) + \cos(x + 3\theta)}$

= $\frac{2\cos(x + \theta)\cos\theta}{2\cos(x + 2\theta)\cos\theta} = \frac{b}{c}$