Question

The value of $\sin 2 x$ is equal to $\left(\right.$ where, $\left.x \neq n \pi+\frac{\pi}{2}\right)$

• A. $2 \sin x \cdot \cos x$
• B. $\frac{2 \tan x}{1+\tan ^2 x}$
• C. Both (a) and (b) are true
• D. None of the above

Answer 1

Answer: (C)

We have, $\sin (x+y)=\sin x \cos y+\cos x \sin y$
On replacing $y$ by $x$, we get
$ \sin 2 x=2 \sin x \cos x$
Again, $ \sin 2 x=\frac{2 \sin x \cos x}{\cos ^2 x+\sin ^2 x}$
On dividing each term by $\cos ^2 x$, we get
$\sin 2 x=\frac{2 \tan x}{1+\tan ^2 x}$