3 x- x x- 3 x is equal to - Vidyadip

MCQ

$\frac{\sin 3 x-\sin x}{\cos x-\cos 3 x}$ is equal to

A
$\cot 2 x$
B
$-\cot 2 x$
C
$-\tan 2 x$
D
$\tan 2 x$

✓

Answer

(a) $\cot 2 x$
Explanation: Using $\sin C -\sin D =2 \cos \frac{(C+D)}{2} \sin \frac{(C-D)}{2}$
and $\cos C -\cos D =-2 \sin \frac{(C+D)}{2} \sin \frac{(C-D)}{2}$, we get
$\frac{\sin 3 x-\sin x}{\cos x-\cos 3 x}=\frac{2 \cos \left(\frac{t}{2}\right) \sin \left(\frac{2 z}{2}\right)}{2 \sin \left(\frac{4 z}{2}\right) \sin \left(\frac{2 z}{2}\right)}=\frac{\cos 2 x \sin x}{\sin 2 x \sin x}=\cot 2 x$.

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