Question

If $x\ne \frac{n\pi }{2}$ and ${\left|\cos x\right|}^{-{\sin }^{2}x-3\sin x+2}=1$ then all solutions of $x$ are given by

• A. $2n\pi +\frac{\pi }{2}$
• B. $(2n+1)\pi -\frac{\pi }{2}$
• C. $n\pi +{(-1)}^n\frac{\pi }{2}$
• D. none of these

Answer 1

Answer: (D)

none of these

${\left|\cos x\right|}^{-{\sin }^{2}x-3\sin x+2}=1$
For equation to hold,
Case I$:|\cos x|=1$
$x=n\pi ,n\in I$
Case II:$|\cos x|\ne 1$
$-{\sin }^{2}x-3\sin x+2=0$