Question

Which of the following sets can be the subset of the general solution of the general solution of $1+\cos 3x=2\cos 2x\left(nϵz\right)$

• A. $n\pi +\frac{\pi }{3}$
• B. $n\pi +\frac{\pi }{8}$
• C. $n\pi -\frac{3\pi }{8}$
• D. $2n\pi$

Answer 1

The correct option is D $2n\pi$

Given, $1+\cos 3x=2\cos 2x$
$1+4{\cos }^{3}x-3\cos x=2(2{\cos }^{2}x-1)=(4{\cos }^{2}x-2)$
$4{\cos }^{3}x-4{\cos }^{2}x-3\cos x+3=0$
$(\cos x-1)(4{\cos }^{2}x-3)=0$
$\cos x=1$ or $\cos x=\frac{\sqrt{3}}{2}$
$\therefore x=2n\pi$ or $x=2n\pi \pm \frac{\pi }{6}$