- Joined
- Jun 27, 2021
- Messages
- 5,386
- Reaction score
- 422
I am having a hard time understanding what needs to be done with proving inverse trigonometric functions. For example, what is she doing in this video lesson?
prove: cos(sin^-1(x))=sqrt(1-x^2)
let sin^-1(x)=y
then cos(sin^-1(x))=cos(y) where -pi/2<= y<= pi/2 , then cos(y) >=0
use identity cos^2(y)+sin^2(y)=1..........solve for cos
cos^2(y)=1-sin^2(y)
cos(y)=sqrt(1-sin^2(y))......since sin^-1(x)=y, we can write that sin(y)=x =>sin^2(y)=x^2
substitute sin^2(y)=x^2 and sin^-1(x)=y in cos(y)=sqrt(1-sin^2(y)) and we have:
cos(sin^-1(x))=sqrt(1-x^2)