Principle Of Mathematical Induction

Question
CBSEENMA11014324

Find the general expression for all the angles whose cotangent is zero.

Solution

Let angle XOP space equals space straight x by any angle, then
                    cot x = 0
rightwards double arrow                      OM over OP equals 0
rightwards double arrow                       OM = 0
rightwards double arrow  OP coincides OY or OY'
i.e.                   space space straight x space equals space plus-or-minus straight pi over 2 comma space plus-or-minus fraction numerator 3 straight pi over denominator 2 end fraction comma space plus-or-minus fraction numerator 5 straight pi over denominator 2 end fraction comma.............
So, general value of x is given by straight x equals left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 comma space straight n space element of space straight Z
                                      

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