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 $\frac{1}{k}$
$\frac{a+c}{b+d}=\frac{k\cos x+k\cos (x+2\theta )}{k\cos (x+\theta )+k\cos (x+3\theta )}$
$=\frac{2\cos (x+\theta )\cos \theta }{2\cos (x+2\theta )\cos \theta }=\frac{\cos (x+\theta )}{\cos (x+2\theta )}=\frac{b}{c}$