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Rodrigues rotation

I do not understand the difference between these two equations:

1. from wikipedia:
wiki Rodrigues formula

2. from open CV doc:
cv2 Rodrigues formal,%20OutputArray%20dst,%20OutputArray%20jacobian)

Where is the cos(θ) gone on the wiki page in the formula 1. ?

Shouln't it be: v_{rot} = cos(θ)v + sin.... ?

Then on the wiki page, there is no more cos(θ) in the definition of R...

Or did I miss something?