If $ 1-\tan ^{2} \theta=\frac{2}{3} $ then what is the value of $ \theta $.
Given:
\( 1-\tan ^{2} \theta=\frac{2}{3} \)
To do:
We have to find the value of \( \theta \).
Solution:
$1-\tan^2 \theta=\frac{2}{3}$
$\tan^2 \theta=1-\frac{2}{3}$
$\tan^2 \theta=\frac{3-2}{3}$
$\tan^2 \theta=\frac{1}{3}$
$\Rightarrow \tan \theta = \frac{1}{\sqrt3}$
$\Rightarrow \theta = 30^o$ (Since $\tan 30^o=\frac{1}{\sqrt3}$)
The value of $\theta$ is $30^o$.
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