The Solution:
Given:
[tex]\begin{gathered} y=\cos\left(2\theta\right)-\sin^2\left(\theta\right)=0 \\ \\ \left\{0\le\theta<360\right\} \end{gathered}[/tex]
The given function has a solution when:
[tex][θ=-35.26438^{\circ\:}+180^{\circ\:}n,\:θ=35.26438^{\circ\:}+180^{\circ\:}n][/tex]
So, the solutions are:
[tex]\begin{gathered} \theta=-35.26438^o+180^o=143.73562^o \\ \\ \theta=-35.26438^o+360^o=323.73562^o \\ \\ \theta=35.26438^o+180^o=215.26438^o \end{gathered}[/tex]
Clearly, the function has 3 solutions in the given iterval.
Therefore, the correct nswrer is [option 3]
