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Question

If $Sin space open parentheses fraction numerator pi Cot space theta over denominator 4 end fraction close parentheses equals Cos space open parentheses fraction numerator pi Tan space theta over denominator 4 end fraction close parentheses$ and $theta$ is in the first quadrant then $theta$ =....

$\frac{π}{3}$
$\frac{π}{2}$
$\frac{π}{4}$
$\frac{π}{6}$

hint Hint:

In this question, we have to find the value of theta if theta is in first quadrant in the equation $Sin space open parentheses fraction numerator pi Cot space theta over denominator 4 end fraction close parentheses equals Cos space open parentheses fraction numerator pi Tan space theta over denominator 4 end fraction close parentheses$ . For this we will make trigonometric identity of both sides equal and then we will equate the sides to get the value of theta.

The correct answer is: $pi over 4$

$sin open parentheses πcotθ over 4 close parentheses equals cos open parentheses πtanθ over 4 close parentheses rightwards double arrow sin open parentheses πcotθ over 4 close parentheses equals sin open parentheses straight pi over 2 minus πtanθ over 4 close parentheses rightwards double arrow πcotθ over 4 equals straight pi over 4 minus πtanθ over 4 rightwards double arrow πcotθ over 4 equals straight pi over 4 open parentheses 2 minus tan theta close parentheses rightwards double arrow c o t theta equals 2 minus t a n theta rightwards double arrow fraction numerator cos theta over denominator sin theta end fraction plus fraction numerator sin theta over denominator cos theta end fraction equals 2 rightwards double arrow fraction numerator cos squared theta plus sin squared theta over denominator sin theta cos theta end fraction equals 2 rightwards double arrow 1 equals 2 sin theta cos theta rightwards double arrow sin straight pi over 2 equals sin 2 theta rightwards double arrow straight pi over 2 equals 2 theta rightwards double arrow theta equals straight pi over 4$

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