If $\sqrt{3}tan5\theta=1$, then find the value of $\theta$.

Given: $\sqrt{3}tan5\theta=1$.

To do: To find the value of $\theta$.
 

Solution: 

As given, $\sqrt{3}tan5\theta=1$

$\Rightarrow tan5\theta=\frac{1}{\sqrt{3}}$

$\Rightarrow tan5\theta=tan30^{o}$                      [$\because tan30^{o}=\frac{1}{\sqrt{3}}$]

$\Rightarrow 5\theta=30^{o}$

$\Rightarrow \theta=\frac{30^{o}}{5}$

$\Rightarrow \theta=6^{o}$

Thus, $\theta=6^{o}$.

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Updated on: 10-Oct-2022

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