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)

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
$tan\theta =tan\alpha$
$\Rightarrow \theta =n\pi +\alpha$