Question

The general value of $\theta$ is obtained from the equation

$\cos 2\theta = \sin\alpha$ is

• A. $2\theta = \frac{\pi}{2} - \alpha$
• B. $\theta = 2n\pi \pm \left( \frac{\pi}{2} - \alpha \right)$
• C. $\theta = \frac{n\pi + ( - 1)^{n}\alpha}{2}$
• D. $\theta = n\pi \pm \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$

Answer 1

Answer: (D)

$\theta = n\pi \pm \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$

Answer 2

$\cos 2\theta = \sin\alpha$ ⇒ $\cos 2\theta = \cos\left( \frac{\pi}{2} - \alpha \right)$

$\therefore 2\theta = 2n\pi \pm \left( \frac{\pi}{2} - \alpha \right)$ ⇒ $\theta = n\pi \pm \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$