Question

find answers between cos2x=cosx Stars given!!

Answer 1

\(\bf cos(2x)= cos(x)\\
\textit{so we know that } cos(2x) = 2cos^2(x)-1\\
2cos^2(x)-1= cos(x) \implies 2cos^2(x)-1-cos(x) = 0\\
2cos^2(x)-cos(x)-1 = 0\)

Answer 2

so is a quadratic equation, then just solve for cos(x)

Answer 3

cos(x) = a
\(\bf 2cos^2(x)-cos(x)-1 = 0 \implies 2a^2-a-1 = 0\)

Answer 4

\(\bf \textit{so we know that } cos(2x) = 2cos^2(x)-1\)
so replace your cos(2x) for that

Answer 5

?

Answer 6

is a trig identity http://www.freemathhelp.com/images/doubleangles.png