If cos⁡xa=cos⁡(x+θ)b=cos⁡(x+2θ)c=cos⁡(x+3θ)d then a+cb+d is equal to

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

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

Solution:

$\begin{array}{l} \frac{a + c}{b + d} = \frac{\cos x + \cos (x + 2 θ)}{\cos (x + θ) + \cos (x + 3 θ)} \\ = \frac{2 \cos (x + θ) \cos θ}{2 \cos (x + 2 θ) \cos θ} = \frac{b}{c} \end{array}$

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