Please explain how to find exact value without the calculator
sec ( tan^-1 5)
Thank you
Hello,
Recall that $\displaystyle 1+\tan^2u=\sec^2u$
So $\displaystyle \sec^2(\tan^{-1}(5))=1+[\tan(\tan^{-1}(5))]^2=1+(5)^2=6$
Now you have to see in which quadrant $\displaystyle \tan^{-1}(5)$ is in order to get the sign of $\displaystyle \sec(\tan^{-1}(5))$
Looks good to you ?