Question

2cos4x+1=0 : FIND ALL SOLUTIONS IN RADIANS IN TERMS OF (PI). please please help.

Answer 1

\[\cos 4x=-\frac{ 1 }{ 2 }=-\cos \frac{ \pi }{ 3 }= \cos \left(2k \pi +\pi-\frac{ \pi }{ 3 } \right),\cos \left(2k \pi+\pi+\frac{ \pi }{3} \right)\]
where k=0,1,2,3
\[\cos 4x=\cos \left( 2k \pi+\frac{ 2\pi }{ 3 } \right),\cos \left( 2k \pi+\frac{ 4\pi }{3 } \right)\]
\[4x=2k \pi+\frac{ 2\pi }{ 3 },2k \pi+\frac{ 5\pi }{ 3 }\]
\[x=\frac{ 2\pi }{ 4 } \left( k+\frac{ 1 }{ 3 } \right),\frac{ 2\pi }{4 }\left( k+\frac{ 4 }{3 } \right)\]