Question

Let $\theta ,\phi ϵ0,2\pi$ be such that
$2cos\theta 1-sin\phi$= $si{n}^2\theta (tan\frac{\theta }{2}+cot\frac{\theta }{2})cos\phi -1$
$tan2\pi -\theta >0$ and $-1<sin\theta <-\frac{\sqrt{3}}{2}$
Then $\phi$ cannot satisfy

• A. $0<\phi <\frac{\pi }{2}$
• B. $\frac{\pi }{2}<\phi <\frac{4\pi }{3}$
• C. $\frac{4\pi }{3}<\phi <\frac{3\pi }{2}$
• D. $\frac{3\pi }{2}<\phi <2\pi$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $0<\phi <\frac{\pi }{2}$
C $\frac{4\pi }{3}<\phi <\frac{3\pi }{2}$
D $\frac{3\pi }{2}<\phi <2\pi$