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If $\cos e c (a - x) = 3$ $\cos e c (3 a + x),$ then $\tan x$ =

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\cot α

\tan α

\tan^{3} α

\tan^{2} α

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detailed solution

Correct option is C

$\cos e c (a - x) = 3 \cos e c (3 a + x)$

$\Rightarrow 3 \sin (a - x) = \sin (3 a + x)$

$\Rightarrow 3 (\sin a \cos x - \cos a \sin x) = \sin 3 a \cos x + \cos 3 a \sin x$

$\Rightarrow \sin x (\cos 3 α + 3 \cos α) = \cos x (3 \sin α - \sin 3 α)$

$\Rightarrow \sin x . 4 \cos^{3} α = \cos x . 4 \sin^{3} α \Rightarrow \tan x = \tan^{3} α$

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If cosec (a-x) = 3cosec (3a+x),then tanx=