Rewrite cos(tan^-1(v)) as an algebraic expression in v.

Question

Can someone help me with this problem? Thanks

Answer 1

1)From definition -->tan(tan^-1(v))=v
2)cos^2(a)=1/(tan^2(a)+1)
cos(a)=+-1/sqrt(tan^2(a)+1)

cos(tan^-1(v))=+-1/sqrt(v^2+1)

Answer 2

thanks for the help

Answer 3

Because -pi/2<tan^-1(v)<pi/2
cos(tan^-1(v))=+1/sqrt(v^2+1) (only +)

Answer 4

Yeah I was looking at that, thanks for clarifing