Question 1202696
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This problem is remarkable.


It is remarkable, because one single example (or "counter-example") is enough to disprove the statement.


And even if a student does not have a calculator, he (or she) must know 
the table values of trigonometric functions.


    In particular,  tan(240°) = {{{sqrt(3)}}}  (in 3rd quadrant), 

    while tan(240°/2) = tan(120°) = {{{-sqrt(3)}}}  (in 2nd quadrant).


This single fact disproves the statement.


<U>ANSWER</U>.  False.
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Solved.


Good problem to learn &nbsp;(may be, &nbsp;for the first time), &nbsp;how counter-examples work in &nbsp;Math.