hello-solve-in-R-tanx-gt-3-please-explain-me-if-possible-

Question Number 76110 by mathocean1 last updated on 23/Dec/19

h e l l o solve in R

\tan x > \sqrt{3}

p l e a s e e x p l a i n m e i f p o s s i b l e .

Answered by MJS last updated on 24/Dec/19

\tan x = \sqrt{3} \land 0 ⩽ x < 2 π

\Rightarrow x = \frac{π}{3} \lor x = \frac{4 π}{3}

but y = \tan x changes its sign at x = 0, x = \frac{π}{2},

x = π and x = \frac{3 π}{2}

\Rightarrow \tan x > \sqrt{3} \Leftrightarrow \frac{π}{3} < x < \frac{π}{2} \lor \frac{4 π}{3} < x < \frac{3 π}{2}

now if x \in R {it}^{'} s the same in each period of length π

\Rightarrow \tan x > \sqrt{3} \Leftrightarrow \frac{π}{3} + n π < x < \frac{π}{2} + n π with n \in Z

Commented by benjo last updated on 24/Dec/19

great sir \dots

Commented by mathocean1 last updated on 24/Dec/19

thank you sir \dots