We know the expression sec^2A-tan^2A=1 using this equation. Given secA+tanA=4 . . (1) (secA+tanA)(secA-tanA)=1 (4)(secA-tanA)=1 (from eq.1) secA-tanA=1/4 . . .(2) Solving eq.1 & eq.2 We get SecA=9/8 & cosA=1/secA=8/9 SecA+cosA=9/8+8/9=145/72. That's it!