How solve the equation for exact solutions in the interval (0,2pi) with 4secx+5=13?

4secx+5=13    subtract 5 from both sides

4secx   =  8       divide both sides by 4

secx  =  2

If the secx  = 2, then cosx = 1/2

And this happens at  x =  pi/3     and x  = 5pi/3

4 sec x +5 = 13

4 sec x = 8

sec x = 2

1/cos x = 2

cos x = 1/2

x = 1.0472 R    5.236 R        or  60 degrees and 300 degrees (pi/3 and 5pi/3)