prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)

please help. I don't even know where to start. (Worried)

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- Sep 30th 2008, 09:18 AMdee18identities (trig)
prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)

please help. I don't even know where to start. (Worried)

- Sep 30th 2008, 09:54 AMChop Suey
$\displaystyle \sin^{-1}{x}$ is an angle. Therefore:

$\displaystyle \sin^{-1}{x} = \theta$

$\displaystyle \Rightarrow x = \sin{\theta}$

Recall that in right triangle trigonometry:

$\displaystyle \sin{\theta} = \frac{\text{opp}}{\text{hyp}}$

You can find the adj side using the Pythagorean theorem. Now we can find $\displaystyle \cos{\theta}$, which is:

$\displaystyle \cos{\theta} = \frac{\text{adj}}{\text{hyp}}$ - Sep 30th 2008, 09:58 AMChop Suey