prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)
please help. I don't even know where to start.
$\displaystyle \sin^{-1}{x}$ 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:
$\displaystyle \cos{\theta} = \frac{\text{adj}}{\text{hyp}}$