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

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

Where:

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

Take the inverse cosine of both sides:

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

Therefore:

$\begin{gathered} x=\frac{3\pi}{4}+\frac{\pi}{7}+2\pi n1 \\ or \\ x=\frac{5\pi}{4}+\frac{\pi}{7}+2\pi n1 \end{gathered}$