Question

The equation $(3+\cos x{)}^2=4-2{\sin }^{8}x$ has

• A. Exactly one solution in $x\in (0,3\pi )$
• B. Exactly three solution
• C. Exactly two solutions $x\in (0,5\pi )$
• D. Infinite solution

Answer 1

Answer: (B)

Exactly three solution

$\begin{array}{c}{\left(3+\cos x\right)}^2=4-2{\sin }^{8}x\\ \ge 4\le 4\\ forsol.toexist:\cos x=-1\sin x=0\\ \Rightarrow x=\pi ,3\pi ,5\pi \\ Hence,optionBisthecorrectanswer.\end{array}$