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
<h3 /><h3>Find SecB</h3>
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
<h3>
</h3><h3>
Find CosB</h3>
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.
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