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

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

Step by step solution

Step 1. Given data

The given equation for verification is

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

Step 2. Proof

As known $\sin^{- 1} (v) + \cos^{- 1} (v) = \frac{π}{2} \dots (1)$

Use Equation $1$ in the given equation

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

as $\sin (\frac{π}{2}) = 1$

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

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

Short Answer

Step by step solution

Step 1. Given data

Step 2. Proof

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