Question

verify cos(sin^- 1 x )=sqrt(1-x^2)

Answer 1

ok

Answer 2

how are you supposed to 'verify' it? a picture will do

Answer 3

i am supposed to type out each step. also i can only mess with one side

Answer 4

ok
\(\sin^{-1}(x)=\theta\iff \theta =\sin(x)\)
then since \(\sin^2(\theta)+\cos^2(\theta)=1\) you get \[\cos^2(\theta)=1-\sin^2(\theta)=1-x^2\]

Answer 5

or if you prefer you can start with
\[\cos^2(\theta)=1-\sin^2(\theta)\] and so
\[\cos^2(\sin^{-1}(x))=1-\sin^2(\sin^{-1}(x))=1-x^2\]

Answer 6

thank you!!!