Solve cos 2v = cos v and sin 2v = sin v

[Maria]

How do I solve these two:

cos 2v = cos v

sin 2v = sin v

 

[plover]

Double angle formulas, e.g. sin 2x = 2(sin x)(cos x)
So your second equation becomes:
2(sin x)(cos x) = sin x

 

[Motifs]

cos2v=2(cosv)^2-1
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]

 

[wm]

How do I solve these two:

(1) cos 2v = cos v

(2) sin 2v = sin v

Does it go like this?

(1) cosv = cos2v = cos( v + v) = cosv cos v - sinv sinv

= cosv [cos v] - [sinv sinv] = cosv[ 1] - [0] 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.