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,theta

\(cos \theta\) = \(PM\over OP\)

\(\therefore\)   \(cos \theta\) = 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.

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