# Math Help - identities (trig)

1. ## identities (trig)

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

2. $\sin^{-1}{x}$ is an angle. Therefore:

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

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

Recall that in right triangle trigonometry:
$\sin{\theta} = \frac{\text{opp}}{\text{hyp}}$

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

$\cos{\theta} = \frac{\text{adj}}{\text{hyp}}$

3. Originally Posted by dee18
prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)
Alternatively, if $y = \cos{(\sin^{-1}{x})}$, then:
$\Rightarrow y^2 = \cos^2{(\sin^{-1}{x})}$
$\Rightarrow y^2 = 1 - \sin^2{(\sin^{-1}{x})}$
$\Rightarrow y = \ldots$