QUESTION

# If $\tan \theta = \tan {240^ \circ }$, then the value of $\theta$ in the first quadrant is ${30^ \circ }$ A. TrueB. False

Hint: Here we have to use the behaviour of tan function in different quadrants and use it to simplify $\tan(240^\circ)$.

We know that $\tan \left( {{{180}^ \circ } + \theta } \right) = \tan \theta$
$\Rightarrow \tan \left( {{{240}^ \circ }} \right) = \tan \left( {{{180}^ \circ } + {{60}^ \circ }} \right) = \tan {60^ \circ }$ $\to$ (1)
$\Rightarrow \tan \theta = \tan {240^ \circ }$
$\Rightarrow \tan \theta = \tan {60^ \circ }$
$\Rightarrow \theta = {60^ \circ }$ (which lies in first quadrant)
Note: In the first quadrant $\theta$ lies between (${0^ \circ }$ to ${90^ \circ }$ ). Carry out the conversion properly. Knowing the behaviour of different trigonometric functions in various quadrants can help solve such problems.