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Q.

If $α, β$ are solutions of $a \cos x + b \sin x = c$ , then $\cos α + \cos β =$

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a

$\frac{2 a c}{c^{2} - a^{2}}$

b

$\frac{2 a c}{a^{2} + b^{2}}$

c

$\frac{c^{2} - a^{2}}{b^{2} + a^{2}}$

d

$\frac{b}{a}$

answer is B.

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Detailed Solution

$a \cos x + b \sin x = c$

$b^{2} (1 - \cos^{2} x) = c^{2} a^{2} \cos^{2} x - 2 a c \cos x + c^{2}$

$(a^{2} + b^{2}) \cos^{2} x - 2 a c \cos x + c^{2} - b^{2} = 0$

$\cos α + \cos β = \frac{2 a c}{a^{2} + b^{2}}$

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