What is the General Solution of $Cos \theta$ = 0 ?

Solution :

The general solution of $cos \theta$ = 0 is given by $\theta$ = $(2n + 1){\pi\over 2}$, n $\in$ Z.

Proof :

We have,

$cos \theta$ = $PM\over OP$

$\therefore$   $cos \theta$ = 0

$\implies$  $OM\over OP$ = 0

$\implies$ OM = 0

$\implies$  OP coincides with OY or OY’

$\implies$  $\theta$ =  $\pm{\pi\over 2}$, $\pm{3\pi\over 2}$, $\pm{5\pi\over 2}$, …….

$\implies$ $\theta$ = $(2n + 1){\pi\over 2}$,  n $\in$ Z

Hence, $\theta$ = $(2n + 1){\pi\over 2}$,  n $\in$ Z is the general solution of $cos \theta$ = 0.