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  4. The most general value of θ satisfying the equations sin θ =sin α and cos θ = cos α is

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Q. The most general value of $ \theta $ satisfying the equations $ sin \,\theta =sin \,\alpha $ and $ cos\,\theta = cos\,\alpha $ is

UPSEEUPSEE 2008

Solution:

Since, $sin\,\theta=sin\,\alpha \dots\left(i\right)$
and $cos\,\theta=cos\,\alpha \dots\left(ii\right)$
On dividing Eq. $\left(i\right)$ by Eq. $\left(ii\right)$, we get
$tan\,\theta=tan\,\alpha$
$\Rightarrow \theta=n\pi+\alpha$