Question

If cos XCOS T T + sin xsin (9 then x can equal: _ Check all that apply. 71 ग +2nI 4 7 A.7+++ B. 34- +27 + 진 C. ग + 4 7 + 1- +27 5+ D. ग +2nT 7 4

Answer 1

`\cos (x)\cdot\cos ((\pi)/(7))+\sin (x)\sin ((\pi)/(7))=-\frac{\sqrt[]{2}}{2}`

Where:

`\begin{gathered} \cos (A-B)=\cos (A)\cos (B)+\sin (A)\sin (B) \\ so\colon \\ \cos (x)\cdot\cos ((\pi)/(7))+\sin (x)\sin ((\pi)/(7))=\cos ((\pi)/(7)-x) \\ \cos ((\pi)/(7)-x)=-\frac{\sqrt[]{2}}{2} \end{gathered}`

Take the inverse cosine of both sides:

`\begin{gathered} (\pi)/(7)-x=2\pi n1+(3\pi)/(4);_{\text{ }}n1\in\Z \\ or \\ (\pi)/(7)-x=2\pi n2+(5\pi)/(4);n2\in\Z \end{gathered}`

Therefore:

`\begin{gathered} x=(3\pi)/(4)+(\pi)/(7)+2\pi n1 \\ or \\ x=(5\pi)/(4)+(\pi)/(7)+2\pi n1 \end{gathered}`