## anonymous 5 years ago Prove that: cos(sin^-1(x)) = sqrt (1-x^2)

1. watchmath

Let $$a=\cos(\sin^{-1} x)$$ Then $$a^2+\sin^2(\sin^{-1}x)=1$$ But remember $$\sin(\sin^{-1}(x))=x$$ Hence $$a^2+x^2=1$$ $$a^2=1-x^2$$ $$a=\sqrt{1-x^2}$$ Therefore $$\cos(\sin^{-1}(x)=\sqrt{1-a^2}$$

2. watchmath

I mean $$\cos(\sin^{-1}(x))=\sqrt{1-x^2}$$

3. anonymous

Do you mind if I ask you another question

4. watchmath

If you think the answer above helps you please the good answer button :). Post your other question as a new question. If it is interesting, I might help you. But don't worry there are a lot of people who will be able to help you :D.

5. anonymous

hello wathmath!

6. anonymous

lots of posts tonight

7. watchmath

wow you already halfway amistre64 medals :D

8. watchmath

I don't know I am not as excited as before in answering questions :D

9. anonymous

well i have to agree. getting old, but my latex is improving by leaps and bounds

10. anonymous

and no amistre is way ahead. i will never catch up

11. watchmath

use \ ( \ ) instead of \ [ \ ] to get inline latex, that will make your post more concise :)

12. anonymous

yo satellite can you go back to this question that you were helping me with? If sin(x) = 1/3 and sec(y) = 5/4 , where x and y lie between 0 and pie/2, evaluate the expression cos(x+y).

13. anonymous

I asked you about how the pathagoras part you did i was a little confused..can you show that work?