Question

If $a=\frac{\sin x\times \cos 3x}{\sin 3x\times \cos x}$ then which of the following is wrong?

• A. $a<\frac{1}{3}$
• B. $a>3$
• C. $\frac{1}{3}<a<3$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{3}<a<3$

Given, $a=\frac{\sin x\times \cos 3x}{\cos x\times \sin 3x}$
It is not defined for
$\cos x=0$ and $\sin 3x=0$
$\Rightarrow x=\frac{(2n+1)\pi }{2}$ and $x=n\pi$
Hence defined for the given range:
$-\frac{2\pi }{3}<x<-\frac{\pi }{2}$ or $-\frac{\pi }{3}<x<0$
Therefore,
$a<\frac{1}{3}$ or $a>3$