Question & Answer
QUESTION

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

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

Complete step-by-step answer:
We know that $\tan \left( {{{180}^ \circ } + \theta } \right) = \tan \theta $
Applying this,
$ \Rightarrow \tan \left( {{{240}^ \circ }} \right) = \tan \left( {{{180}^ \circ } + {{60}^ \circ }} \right) = \tan {60^ \circ }$ $\to$ (1)
According to question,
$ \Rightarrow \tan \theta = \tan {240^ \circ }$
So from (1),
$ \Rightarrow \tan \theta = \tan {60^ \circ }$
So on comparing,
$ \Rightarrow \theta = {60^ \circ }$ (which lies in first quadrant)
So, your given problem statement is False.
Hence option B is correct.

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.