Question

Let A be the set containing value(s) of $x$ which satisfy the equation $3{\sin }^{2}x-\cos x=\sin x(3\cos x-1)$, where $x\in [0,9\pi ]$, then the correct statement(s) is/are -

• A. Number of elements in set A is $17$
• B. Number of elements in set A is $18$
• C. Sum of elements in set A is $\frac{297}{4}\pi$
• D. Sum of elements in set A is $\frac{295}{4}\pi$

Answer 1

Answer: (A), (C)

Sum of elements in set A is $\frac{297}{4}\pi$

$3{\sin }^{2}x-\cos x-3\sin x\cos x+\sin x=0$

$(\sin x-\cos x)(3\sin x+1)=0$

$\sin x=-\frac{1}{3}$ or $\tan x=1$

$A=\{\pi +\theta ,2\pi -\theta ,3\pi +\theta ,4\pi -\theta ,5\pi +\theta ,6\pi -\theta ,7\pi +\theta ,8\pi -\theta ,\frac{\pi }{4},\frac{5\pi }{4},\dots \dots \dots \frac{33\pi }{4}\}(\text{where}\theta ={\sin }^{-1}\frac{1}{3})$
Total $17$ solutions

Sum $=\frac{297\pi }{4}$