Question

can someone plz help!
Find all solutions of the equation in the interval [0,2pi)
2cos(x+pi)+2cos(x-pi)=0
the answers r supposed to be pi over 2 and 3pi over 2 i dont get it!

Answer 1

\[2[\cos(x)\cos(\pi)-\sin(x) \sin(\pi)]+2[\cos(x)\cos(\pi)+\sin(x) \sin(\pi)]\]
\[=2[-\cos(x)]+2[-\cos(x)]=-2\cos(x)-2\cos(x)=-4\cos(x)=0\]

Answer 2

\[=> \cos(x)=0\]
I will leave the rest to you :)

Answer 3

thnx a million!:))))))))