Question

Use an identity to solve the following equation on the interval [0,2pi) cos2x=cosx-1

Answer 1

\[\cos 2x=\cos x-1,1+\cos 2 x=\cos x\]
\[2 \cos ^2x=\cos x,\cos~ x ~\left( 2 \cos x-1 \right)=0\]
solve

Answer 2

Can you help elaborate more? Do you then use the unit circle or do you find the zeros and ones for cosx?

Answer 3

\[\cos x=0=\cos \frac{ \pi }{ 2 } ,\cos \frac{ 3 \pi }{ 2 },x=?\]

Answer 4

\[2 \cos x=1,\cos x=\frac{ 1 }{ 2 }=\cos \frac{ \pi }{ 3 },\cos \left( 2 \pi-\frac{ \pi }{ 3 } \right)\]
x=?

Answer 5

Okay, I got it! Thank you(:

Answer 6

yw