Chapter 7: Q. 88 (page 496)

In Problems 79-90, find the exact value of each expression.
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$

Short Answer

Expert verified

The exact value is $\frac{9}{10}$

Step by step solution

Given information

Given expression $\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$

Use half angle formula and calculate

Here,

$\cos^{2} (\frac{θ}{2}) = \frac{1 + \cos θ}{2} \cos (\cos^{- 1} x) = x \cos^{- 1} x = \sin^{- 1} (\sqrt{1 - x^{2}}) a = \cos^{2} (\frac{1}{2} \sin^{- 1} (\frac{3}{5})) θ = \sin^{- 1} (\frac{3}{5}) θ = \cos^{- 1} (\frac{4}{5})$

Calculating using half angle formula

Calculating, we get

$a = \cos^{2} (\frac{1}{2} \sin^{- 1} (\frac{3}{5})) a = \frac{1 + \cos (\cos^{- 1} (\frac{4}{5}))}{2} a = = \frac{1 + \frac{4}{5}}{2} a = \frac{9}{10}$

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In Problems 79-90, find the exact value of each expression.
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$

Short Answer

Step by step solution

Given information

Use half angle formula and calculate

Calculating using half angle formula

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Short Answer

Step by step solution

Given information

Use half angle formula and calculate

Calculating using half angle formula

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In Problems 79-90, find the exact value of each expression.
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$
$\cos^{2} (\frac{1}{2} \sin^{- 1} \frac{3}{5})$