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Chapter 7: Q. 81 (page 496)

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

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

Assume θ=sin-135 and use double angle formula

Using double angle, we get

$\cos (2 θ) = 1 - 2 {(\frac{3}{5})}^{2} \cos (2 θ) = 1 - 2 \cdot \frac{9}{25} \cos (2 θ) = \frac{7}{25}$

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Most popular questions from this chapter

In Problems 9–36, find the exact value of each expression.

$\cos (\sin^{- 1} \frac{\sqrt{2}}{2})$

True or False:

$\tan 2 θ + \tan 2 θ = \tan (4 θ)$

Find the value of the number C:

$\frac{1}{2} \cos^{2} x + C = \frac{1}{4} \cos (2 x)$

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .

Show that $\tan^{- 1} v + c o t^{- 1} v = \frac{π}{2}$

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