I need to find the points of intersection of sin 2x and sin 4x in degrees. I can do this kind of question but this one is difficult.
Use the identities for sin(4x) and sin(2x)
$\displaystyle \sin(4x) = 4\sin(x) \cos^3(x) - 4\sin^3(x) \cos(x) = 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x))$
$\displaystyle \sin(2x) = 2 \sin(x) \cos(x)$
$\displaystyle 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) = 2 \sin(x) \cos(x)$
$\displaystyle 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) - 2 \sin(x) \cos(x) = 0$
$\displaystyle [2 \sin(x) \cos(x)][2cos(2x)+1] = 0$
Either $\displaystyle \sin(x) = 0$, $\displaystyle \cos(x) = 0$ or $\displaystyle 2\cos(2x)+1 = 0$