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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS2 Marks
Question
Find the principal solution of the equation tan x = $\frac { - 1 } { \sqrt { 3 } }$
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Answer

Given, $tan\ x =$ $\frac { - 1 } { \sqrt { 3 } }$
Here, value of $tan\ x$ is negative. So, x lies in II and IV quadrants.
As we know, $tan$ $\frac { \pi } { 6 }$ = $\frac { - 1 } { \sqrt { 3 } }$
$\therefore$ $tan$ $\left( \pi - \frac { \pi } { 6 } \right)$ = - $\frac { 1 } { \sqrt { 3 } }$ $\Rightarrow$ tan $\frac { 5 \pi } { 6 } = \frac { - 1 } { \sqrt { 3 } }$
$\therefore$ $x =$ $\frac { 5 \pi } { 6 }$, which lies in I quadrant.
$tan$ $\left( 2 \pi - \frac { \pi } { 6 } \right)$ = - tan $\frac { \pi } { 6 }$
$\Rightarrow$ tan $\frac { 11 \pi } { 6 } = - \frac { 1 } { \sqrt { 3 } }$
$\therefore$ $x =$ $\frac { 11 \pi } { 6 }$, which lies in IV quadrant.
$\therefore$ principal solutions are $x =$ $\frac { 5 \pi } { 6 }$ and $x =$ $\frac { 11 \pi } { 6 }$.

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