Question

if cos 2alpha=sin alpha then value of tan 2alpha is​

Answer 1

Correct answer is $\tan 2 \alpha = \tan (\frac{\pi}{3})$ $= \sqrt{3}$

Explanation:

Given that, $\cos 2\alpha = \sin \alpha$

⇒ $\tan 2\alpha =$ ?

We know that, $\cos 2 \alpha = sin (\frac{\pi}{2} - 2 \alpha)$

So, $\sin(\frac{\pi}{2} - 2 \alpha) = \sin \alpha$

⇒ $\frac{\pi}{2} - 2 \alpha = \alpha$

⇒ $3 \alpha = \frac{\pi}{2}$

⇒ $2\alpha = \frac{\pi}{3}$

Hence, $\tan 2 \alpha = \tan (\frac{\pi}{3})$ $= \sqrt{3}$.