Question

If $2 \cos x < \sqrt { 3 }$ and $x \in [ - \pi , \pi ]$then the solution set for x is

• A. $\left[ - \pi , \frac { - \pi } { 6 } \right) \cup \left( \frac { \pi } { 6 } , \pi \right]$
• B. $\frac { - \pi } { 6 } , \frac { \pi } { 6 }$
• C. $\left[ - \pi , \frac { - \pi } { 6 } \right] \cup \left[ \frac { \pi } { 6 } , \pi \right]$
• D. None of these

Answer 1

Answer: (A)

$\left[ - \pi , \frac { - \pi } { 6 } \right) \cup \left( \frac { \pi } { 6 } , \pi \right]$

Answer 2

Here, The value scheme for this is shown below.

From the figure,

$- \pi \leq x < \frac { - \pi } { 6 }$ or $\frac { \pi } { 6 } < x \leq \pi$

$\therefore$ $x \in \left[ - \pi , \frac { - \pi } { 6 } \right) \cup \left( \frac { \pi } { 6 } , \pi \right]$.