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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 101 (page 487)

Show that $\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$

Short Answer

Expert verified

The equation $\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$ can be obtained as

$\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = \sin (\frac{蟺}{2}) \sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$

Step by step solution

01

Step 1. Given data

The given equation for verification is

$\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$

02

Step 2. Proof

As known $\sin^{- 1} (v) + \cos^{- 1} (v) = \frac{蟺}{2} 鈰� (1)$

Use Equation $1$ in the given equation

$\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = \sin (\frac{蟺}{2})$

as $\sin (\frac{蟺}{2}) = 1$

So $\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$

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