Question

If $\frac{1}{6}\sin x,\cos x,\tan x$ are in G.P then

• A. $n\pi \pm \frac{\pi }{3},n\in Z$
• B. $2n\pi \pm \frac{\pi }{3},n\in Z$
• C. $n\pi \pm (-1{)}^n\frac{\pi }{3},n\in Z$
• D. $n\pi \pm \frac{\pi }{6},n\in Z$

Answer 1

The correct option is B $2n\pi \pm \frac{\pi }{3},n\in Z$

${\cos }^{2}x=\frac{1}{6}\sin x\tan x6{\cos }^{2}x=\frac{{\sin }^{2}x}{\cos x}6{\cos }^{3}x=1-{\cos }^{2}x6{\cos }^{3}x+{\cos }^{2}x=1\therefore \cos x=\frac{1}{2}\therefore \cos x=\cos \frac{\pi }{3}\therefore x=2n\pi \pm \frac{\pi }{3},n\in Z$