# Write the trigonometric expression as an algebraic expression. sin(arcsin x + arccos x)?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

4
dk_ch Share
Aug 1, 2016

Let ${\sin}^{-} 1 x = A$
$\implies x = \sin A = \cos \left(\frac{\pi}{2} - A\right)$

$\implies {\cos}^{-} 1 x = \frac{\pi}{2} - A = \frac{\pi}{2} - {\sin}^{-} 1 x$

${\sin}^{-} 1 x + {\cos}^{-} 1 x = \frac{\pi}{2}$

So the given expression

$\sin \left({\sin}^{-} 1 x + {\cos}^{-} 1 x\right) = \sin \left(\frac{\pi}{2}\right) = 1$

Alternative way

$\sin \left({\sin}^{-} 1 x + {\cos}^{-} 1 x\right)$

$= \left(\sin {\sin}^{-} 1 x\right) \left(\cos {\cos}^{-} 1 x\right) + \left(\cos {\sin}^{-} 1 x\right) \left(\sin {\cos}^{-} 1 x\right)$

$= x \cdot x + \left(\cos {\cos}^{-} 1 \sqrt{1 - {x}^{2}}\right) \left(\sin {\sin}^{-} 1 \sqrt{1 - {x}^{2}}\right)$

$= {x}^{2} + 1 - {x}^{2} = 1$

• 9 minutes ago
• 15 minutes ago
• 15 minutes ago
• 15 minutes ago
• 3 minutes ago
• 5 minutes ago
• 5 minutes ago
• 5 minutes ago
• 6 minutes ago
• 7 minutes ago
• 9 minutes ago
• 15 minutes ago
• 15 minutes ago
• 15 minutes ago