Chapter 7: Q. 86 (page 496)

In Problems 79-90, find the exact value of each expression.
$\cos [2 \tan^{- 1} (- \frac{4}{3})]$

Short Answer

Expert verified

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

Step by step solution

Given information

Given expression $\cos [2 \tan^{- 1} (- \frac{4}{3})]$

Use double angle formula and calculate the value

Here, $\cos (2 θ) = 2 \cos^{2} θ - 1$

$\cos (\cos^{- 1} x) = x \tan^{- 1} x = \cos^{- 1} (\frac{1}{\sqrt{1 + x^{2}}})$

$a = \cos (2 \tan^{- 1} (- \frac{4}{3})) θ = \tan^{- 1} (- \frac{4}{3}) θ = \cos^{- 1} (\frac{3}{5})$

Using double angle formula

Using, we get

$a = \cos (2 \tan^{- 1} (- \frac{4}{3})) a = = 2 \cos^{2} (\cos^{- 1} (\frac{3}{5})) - 1 a = 2 {(\frac{3}{5})}^{2} - 1 a = \frac{- 7}{25}$

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In Problems 79-90, find the exact value of each expression.
$\cos [2 \tan^{- 1} (- \frac{4}{3})]$

Short Answer

Step by step solution

Given information

Use double angle formula and calculate the value

Using double angle formula

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In Problems 79-90, find the exact value of each expression.cos2tan-1-43

Short Answer

Step by step solution

Given information

Use double angle formula and calculate the value

Using double angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Probability and Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 79-90, find the exact value of each expression.
$\cos [2 \tan^{- 1} (- \frac{4}{3})]$