If cosxcosy=2 and cos(x−y)=32 , then tany=

cosxcosy=2 cos(x−y)=32 x−y=30°→(1) ⇒cos(30°+y)cosy=2 ⇒32cosy−12sinycosy=2 ⇒32−tany2=2 3−tany=4 ⇒3−4=tany

cosxcosy=2 cos(x−y)=32 x−y=30°→(1) ⇒cos(30°+y)cosy=2 ⇒32cosy−12sinycosy=2 ⇒32−tany2=2 3−tany=4 ⇒3−4=tany

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If $\frac{\cos x}{\cos y} = 2$ and $\cos (x - y) = \frac{\sqrt{3}}{2}$ , then $\tan y =$

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\sqrt{3} - 4

\sqrt{3} + 1

\sqrt{3} - 1

\sqrt{3} + 4

answer is C.

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\frac{\cos x}{\cos y} = 2

$\cos (x - y) = \frac{\sqrt{3}}{2}$

$x - y = 30 ° \to (1)$

$\Rightarrow \frac{\cos (30 ° + y)}{\cos y} = 2$

$\Rightarrow \frac{\frac{\sqrt{3}}{2} \cos y - \frac{1}{2} \sin y}{\cos y} = 2$

$\Rightarrow \frac{\sqrt{3}}{2} - \frac{\tan y}{2} = 2$

$\sqrt{3} - \tan y = 4$

$\Rightarrow \sqrt{3} - 4 = \tan y$

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