Question

Prove that:

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

Answer 1

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 \(\cos(\sin^{-1}(x)=\sqrt{1-a^2}\)

Answer 2

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

Answer 3

Do you mind if I ask you another question

Answer 4

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.

Answer 5

hello wathmath!

Answer 6

lots of posts tonight

Answer 7

wow you already halfway amistre64 medals :D

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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).

Answer 13

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