Maths-
General
Easy

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 =

  1. open curly brackets fraction numerator negative pi over denominator 3 end fraction comma pi over 4 close curly brackets
  2. open curly brackets pi over 3 comma fraction numerator negative pi over denominator 4 end fraction close curly brackets
  3. open curly brackets pi over 6 comma fraction numerator negative pi over denominator 3 end fraction close curly brackets
  4. open curly brackets fraction numerator negative pi over denominator 12 end fraction comma pi over 12 close curly brackets

hintHint:

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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