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Question

If $Tan squared space theta equals square root of 3 plus left parenthesis square root of 3 minus 1 right parenthesis Tan space theta$ and $theta$ lies in $open parentheses negative pi over 2 comma pi over 2 close parentheses$ then $theta$ =

$\{\frac{- π}{3}, \frac{π}{4}\}$
$\{\frac{π}{3}, \frac{- π}{4}\}$
$\{\frac{π}{6}, \frac{- π}{3}\}$
$\{\frac{- π}{12}, \frac{π}{12}\}$

hint Hint:

in this question, we have to find the value of $ϑ$ . Firstly, we will simplify the equation and as it is given that the value will lie between $open parentheses fraction numerator negative pi over denominator 2 end fraction comma pi over 2 close parentheses$ , so we can find the required solution.

The correct answer is: $open curly brackets pi over 3 comma fraction numerator negative pi over denominator 4 end fraction close curly brackets$

$space space space space t an squared space theta equals square root of 3 plus left parenthesis square root of 3 minus 1 right parenthesis t an space theta rightwards double arrow tan squared theta minus square root of 3 tan space theta minus tan space theta minus square root of 3 equals 0 rightwards double arrow tan space theta left parenthesis tan space theta minus square root of 3 right parenthesis space plus space left parenthesis tan space theta space minus square root of 3 right parenthesis equals 0 rightwards double arrow open parentheses tan space theta plus 1 close parentheses open parentheses tan space theta minus square root of 3 close parentheses equals 0 rightwards double arrow tan space theta equals equals negative 1 space o r space tan space theta space equals square root of 3 rightwards double arrow tan space theta space equals tan space open parentheses fraction numerator negative pi over denominator 4 end fraction close parentheses space o r space tan space theta space equals tan pi over 3 space space space space space space space space space space open square brackets a s space theta space l i e s space i n space open parentheses fraction numerator negative pi over denominator 2 end fraction comma pi over 2 close parentheses close square brackets rightwards double arrow theta equals fraction numerator negative pi over denominator 4 end fraction o r pi over 3 S o comma space open curly brackets fraction numerator negative pi over denominator 4 end fraction comma pi over 3 close curly brackets$

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