Question

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

• A. $2n\pi +\alpha$
• B. $2n\pi -\alpha$
• C. $n\pi +\alpha$
• D. $n\pi -\alpha$

Answer 1

Answer: (C)

$n\pi +\alpha$

We have given that

$\sin \theta =\sin \alpha ----\left(i\right)$

$\cos \theta =\cos \alpha ----\left(ii\right)$

On dividing (i) and (ii) , we get

$\Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{\sin \alpha }{\cos \alpha }$

$\Rightarrow \tan \theta =\tan \alpha$

$\therefore \theta =n\pi +\alpha$