Solution : The general solution of \(tan^2 \theta\) = \(tan^2 \alpha\) is given by \(\theta\) = \(n\pi \pm \alpha\), n \(\in\) Z. Proof : We have, \(tan^2 \theta\) =\(tan^2 \alpha\) \(\implies\)  \(1 – tan^2\theta\over 1 + tan^2 \theta\) =\(1 – tan^2\alpha\over 1 + tan^2 \alpha\) \(\implies\)   \(cos 2\theta\) = \(cos 2\alpha\) \(\implies\)  \(2\theta\) = \(2n\pi […]

Solution : The general solution of \(cot \theta\) = 0 is given by \(\theta\) = \((2n + 1){\pi\over 2}\), n \(\in\) Z. Proof : We have, \(cot \theta\) = \(OM\over PM\) \(\therefore\)   \(cot \theta\) = 0 \(\implies\)  \(OM\over PM\) = 0 \(\implies\) OM = 0 \(\implies\)  OP coincides with OY or OY’ \(\implies\)  \(\theta\) =

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’ \(\implies\)  \(\theta\) = 

Solution : The general solution of \(tan \theta\) = 0 is given by \(\theta\) = \(n\pi\), n \(\in\) Z. Proof : We have, \(tan \theta\) = \(PM\over OM\) \(\therefore\)   \(tan \theta\) = 0 \(\implies\)  \(PM\over OM\) = 0 \(\implies\) PM = 0 \(\implies\)  OP coincides with OX or OX’ \(\implies\)  \(\theta\) = 0, \(\pi\), \(2\pi\),

Solution : The general solution of \(sin \theta\) = 0 is given by \(\theta\) = \(n\pi\), n \(\in\) Z. Proof : We have, \(sin \theta\) = \(PM\over OP\) \(\therefore\)   \(sin \theta\) = 0 \(\implies\)  \(PM\over OP\) = 0 \(\implies\) PM = 0 \(\implies\)  OP coincides with OX or OX’ \(\implies\)  \(\theta\) = 0, \(\pi\), \(2\pi\),