The value of cosB ≅ 0.447 to three decimal places.
Since angle A and angle B are acute and tanB = 2, we find cosB from the trigonometric identity
tan²B + 1 = sec²B
Find SecB
So, substituting the value of tanB into the equation, we have
tan²B + 1 = sec²B
2² + 1 = sec²B
4 + 1 = sec²B
5 = sec²B
Taking square root of both sides, we have
√sec²B = ±√5
secB = ±√5
Find CosB
Since secB = 1/cosB, we have that
1/cosB = ±√5
⇒cosB = ±1/√5
Since B is acute, cosB will be positive.
So, cosB = 1/√5
cosB = 1/2.2361
cosB = 0.4472
cosB ≅ 0.447 to three decimal places.
So, the value of cosB ≅ 0.447 to three decimal places.
Learn more about cosine here:
https://brainly.com/question/10417664
