Evaluate:
i) `sin(cos^(-1)(3/5))`,
ii) `cos(tan^(-1)(3/4))`

Explanation

i) Let `cos^(-1)3/5=theta`, where `theta in [0, pi]`.
Then, `costheta=3/5`.
Since, `theta in [0,pi]`, we have `sin theta gt 0`.
`therefore sintheta=sqrt(1-cos^(2)theta)=sqrt(1-9/25)=sqrt(16/25)=4/5`.
Hence, `sin(cos^(-1)3/5)=sin theta=4/5`.
ii) Let `tan^(-1)3/4=theta`, where `theta in (-pi/2, pi/2)`.
Then, `tantheta=3/4`.
Since, `theta in (-pi/2, pi/2)`, so `costheta gt 0`.
`therefore costheta=1/(sec theta) = 1/sqrt(1+tan^(2)theta)=1/sqrt(1+9/16)=sqrt(16/25)=4/5`.