Question

If tan A + sec A = 4, find sin A + cos A

Answer 1

tanA+secA=4

secA=4-tanA

Squaring both sides

sec²A=16+tan²A-8tanA

sec²A-tan²A=16-8tanA

1=16-8tanA

8tanA=15

tanA=15/8

tan²A=sec²A-1

225/64=sec²A-1

sec²A=289/64

secA=17/8

cosA=1/secA

        =8/17

sin²A+cos²A=1

sin²A=1-64/289

sin²A=225/289

sinA=15/17

sinA+cosA=15/17+8/17

                 =23/17