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  4. If tan( α + β) = √3 , tan( α -β) = 1 then tan 6β

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Q. If $\tan( \alpha + \beta) = \sqrt{3} , \tan( \alpha -\beta) = 1$ then $\tan 6\beta$

Trigonometric Functions

Solution:

Let $\left(\alpha + \beta\right) =60^{\circ}$
$\left(\alpha - \beta\right) =45^{\circ}$
$\Rightarrow \, 2 \beta = 15^{\circ}$
$\Rightarrow \, 6 \beta = 45^{\circ}$