How do I solve these two:
cos 2v = cos v
sin 2v = sin v
Double angle formulas, e.g. sin 2x = 2(sin x)(cos x)
So your second equation becomes:
2(sin x)(cos x) = sin x
t=cosv and solve equation.
The second I remmember you already asked and were properly answered by matt and mods, so why "repeat" it ?
[dont forget to choose only t's in the range [-1,1] only]
Does it go like this?
(1) cosv = cos2v = cos( v + v) = cosv cos v - sinv sinv
= cosv [cos v] - [sinv sinv] = cosv[ 1] -  if it is to equal cosv, as given.
Therefore need: [cosv] = 1 and [sinv] = 0; so v = 0.
[PS: Your teacher may prefer Motifs' suggestion where you solve a standard quadratic equation.]
(2) is similar, but more interesting. Good luck.
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