Question

if `tan^(-1)(4/3)=theta`, find the value of `costheta`.

Answer 1

`tan^(-1)4/3=theta`, where `theta in (-pi/2,pi/2)`.
`therefore tantheta=4/3`.
We know that `costheta gt 0`, when `theta=(-pi/2,pi/2)`.
`therefore costheta=1/(sectheta)=1/sqrt(1+tan^(2)theta)=1/sqrt(1+16/9)=3/5`.