+69 Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4 cos^3 x = 4 cos x
+6250 Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4 cos^3 x = 4 cos x
\(4 \cos^3(x) = 4\cos(x)\\ \\ \cos^3(x) = \cos(x)\)
\(\text{If }\cos(x) \neq 0 \\ \\ \cos^2(x)=1 \\ \\ \cos(x)=\pm 1\\ \\ x = 0, \pi\)
\(\text{If }\cos(x)=0 \\ \\ x=\dfrac \pi 2, \dfrac {3\pi}{2}\)
so the full set of solutions is
\(x=\left \{0, \dfrac \pi 2, \pi, \dfrac {3\pi}{2}\right \}\)
+6250 Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4 cos^3 x = 4 cos x
\(4 \cos^3(x) = 4\cos(x)\\ \\ \cos^3(x) = \cos(x)\)
\(\text{If }\cos(x) \neq 0 \\ \\ \cos^2(x)=1 \\ \\ \cos(x)=\pm 1\\ \\ x = 0, \pi\)
\(\text{If }\cos(x)=0 \\ \\ x=\dfrac \pi 2, \dfrac {3\pi}{2}\)
so the full set of solutions is
\(x=\left \{0, \dfrac \pi 2, \pi, \dfrac {3\pi}{2}\right \}\)
