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Chapter 7: Q. 82 (page 496)

In Problems 79-90, find the exact value of each expression.
$\cos (2 \cos^{- 1} \frac{4}{5})$

Short Answer

Expert verified

The exact value is $\frac{7}{25}$

Step by step solution

01

Given information

Given expression $\cos (2 \cos^{- 1} \frac{4}{5})$

02

Step 2:Assume θ=cos-145and use double angle formula

Using double angle, we get

$\cos (2 θ) = 2 {(\frac{4}{5})}^{2} - 1 \cos (2 θ) = \frac{32}{25} - 1 \cos (2 θ) = \frac{7}{25}$

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