Can someone kindly explain? Thanks

[whatisphysics]

Homework Statement

I have attached my question. I don't understand how A can turn into B? (the highlighted parts)

Homework Equations

The Attempt at a Solution

I finished the whole question, but I don't understand why arcsec turns into arctan...

 

[Mark44]

Draw a right triangle with acute angle α at the left and another acute angle β at the upper right. Label the hypotenuse as x and the base as 4. Then the altitude is sqrt(x² - 16).

Then x/4 = sec(α), so α = sec^-1(x/4).

And 4/sqrt(x² - 16) = tan(β), so β = tan^-1( 4/sqrt(x² - 16)).

What can you say about the angles α and β?