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3.Trigonometrical Ratios, Functions and Identities
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If $\frac{{\cos x}}{a} = \frac{{\cos (x + \theta )}}{b} = \frac{{\cos (x + 2\theta )}}{c} = \frac{{\cos (x + 3\theta )}}{d} \, ,$ then $\left( {\frac{{a + c}}{{b + d}}} \right)$ is equal to :-
A
$\frac{a}{d}$
B
$\frac{c}{d}$
C
$\frac{b}{c}$
D
$\frac{d}{a}$
Solution
Correct Answer – C
For each of the ratios be $1 / k$.
$\frac{a+c}{b+d}=\frac{k \cos x+k \cos (x+2 B)}{k \cos (x+\theta)+k \cos (x+3 \theta)}$
$=\frac{2 \cos (x+\theta) \cos \theta}{2 \cos (x+2 \theta) \cos \theta}$
$=\frac{\cos (x+\theta)}{\cos (x+2 \theta)}=\frac{b}{c}$
Standard 11
Mathematics
