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Question

If , then $Tan space theta plus Sec space theta equals square root of 3$ he principal value of $open parentheses theta plus pi over 6 close parentheses$ is

$\frac{π}{3}$
$\frac{π}{4}$
$\frac{2 π}{3}$
$\frac{π}{2}$

hint Hint:

In the question we have to find the value of $theta plus straight pi over 6$ in $Tan space theta plus Sec space theta equals square root of 3$ . For this we will make the trigonometric identity of both the sides equal then we will equate the sides to get the value.

The correct answer is: $pi over 3$

$Tan space theta plus Sec space theta equals square root of 3 rightwards double arrow fraction numerator s i n theta over denominator cos theta end fraction plus fraction numerator 1 over denominator cos theta end fraction equals square root of 3 rightwards double arrow sin theta plus 1 equals square root of 3 cos theta rightwards double arrow square root of 3 cos theta minus sin theta equals 1 rightwards double arrow fraction numerator square root of 3 over denominator 2 end fraction cos theta minus 1 half sin theta equals 1 half rightwards double arrow cos straight pi over 6 cos theta minus sin straight pi over 6 sin theta equals 1 half rightwards double arrow cos open parentheses straight pi over 6 plus theta close parentheses equals cos straight pi over 3 rightwards double arrow theta plus straight pi over 6 equals straight pi over 3$

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