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

Answer 1

Answer: (C)

Let each of the ratio be $\frac{1}{ k }$
$\frac{a+c}{b+d}=\frac{k \cos x+k \cos (x+2 \theta)}{k \cos (x+\theta)+k \cos (x+3 \theta)}$
$=\frac{2 \cos (x+\theta) \cos \theta}{2 \cos (x+2 \theta) \cos \theta}=\frac{\cos (x+\theta)}{\cos (x+2 \theta)}=\frac{b}{c}$