Maths-
General
Easy

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 =....

  1. pi over 3
  2. pi over 2
  3. pi over 4
  4. pi over 6

Hint:

In this question, we have to find the value of theta if theta is in first quadrant in the equationSin 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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