Question

The equation $(3+cosx{)}^2=4-2si{n}^{8}x$ has

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

Answer 1

The correct option is A exactly one solution in $xϵ(0,3\pi )$

$4\le LHS\le 16$ and $2\le RHS\le 4$

$\Rightarrow LHS=RHS=4$

$\Rightarrow \cos x=-1$

$\Rightarrow x=(2n+1)\pi$

$\Rightarrow x=\pi ,3\pi$

Hence there is exactly one solution in $x\in (0,3\pi )$