Question

Sin3x/sinx=k,find the value of tan3x/tanx in terms of k

Answer 1

Given :

$\frac{ \sin(3x) }{ \sin(x) } = k$

Identities :

$\tan = \frac{ \sin }{ \cos}$

Solution :

$= > \frac{ \tan</u><u> </u><u>3x }{ \tan</u><u> </u><u>x} \\ \\ = > \frac{\frac{ \sin</u><u> </u><u>3x }{ \cos} }{ \frac{ \sin</u><u> </u><u>x }{ \cos } } \\ \\ = > \frac{ \sin</u><u> </u><u>3x }{ \cos } \times \frac{ \cos}{ \sin</u><u> </u><u>x} \\ \\</u><u> </u><u> = > \frac{ \sin</u><u> </u><u>3x }{ \sin</u><u> </u><u>x</u><u> </u><u>} \\ \\ = > \: \: \: k$

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