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Solution 4.3:4d
From Förberedande kurs i matematik 1
With the formula for double angles and the Pythagorean identity
cos2v+sin2v=1, we can express
cos 2v
in terms of
cos v,
cos 2v=cos2v−sin2v=cos2v−
1−cos2v
=2cos2v−1=2b2−1