Answer:
cos(B/2) = 2√5 / 5
Step-by-step explanation:
Use half angle formula:
cos²(B/2) = (1 + cos B) / 2
cos²(B/2) = (1 + 3/5) / 2
cos²(B/2) = (8/5) / 2
cos²(B/2) = 4/5
cos(B/2) = 2/√5
cos(B/2) = 2√5 / 5
The answer is cos(B/2) = 2√5 / 5
Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]
Given: If cos B = 3/5, then the positive value of cos 1/2 B, in simplest radical form with a rational denominator:
on using the half-angle formula of cosine:
cos²(B/2) = (1 + cos B) / 2
put value of cos B =3/5 (given)
cos²(B/2) = (1 + 3/5) / 2
on simplyfying
cos²(B/2) = (8/5) / 2
cos²(B/2) = 4/5
on taking underroot we get
cos(B/2) = 2/√5
in simplest radical form with a rational denominator
hence, cos(B/2) = 2√5 / 5
Learn more about the half-angle formula of cosine: https://brainly.com/question/2146681
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