With-the-help-of-graph-find-the-solution-set-of-inequation-tan-x-gt-3-

Question Number 15301 by Tinkutara last updated on 09/Jun/17

With the help of graph, find the

solution set of inequation \tan x > - \sqrt{3} .

Answered by mrW1 last updated on 09/Jun/17

x \in (n π - \frac{π}{3}, n π + \frac{π}{2}) \land n \in Z

Commented by Tinkutara last updated on 10/Jun/17

But answer is [n π - \frac{π}{3} < x < n π + \frac{π}{2}]

\cup {n π + \frac{2 π}{3} < x < n π + \frac{3 π}{2}}

Your first set is correct but how to get

the 2^{nd} set in union ?

Commented by mrW1 last updated on 10/Jun/17

the second set is the same as the first .

{n π + \frac{2 π}{3} < x < n π + \frac{3 π}{2}}

\equiv {(n + 1) π - \frac{π}{3} < x < (n + 1) π + \frac{π}{2}}

\equiv {m π - \frac{π}{3} < x < m π + \frac{π}{2}}

since n \in Z, in set 1 is set 2 included .

Commented by Tinkutara last updated on 10/Jun/17

Thanks Sir!