The angle A is such that

secA + tanA = 2

Show that

secA-tanA=1/2

Hence, find the exact value of cosA.

1 / cos A + sin A / cos A = 2

(1 + sin A) / cos A = 2

1 + sin A = 2 cos A

sin A = 2 cos A - 1

sin² A + cos² A = 1

(2 cos A - 1) ² + cos² A = 1

4 cos² A - 4 cos A + 1 + cos² A = 1

5 cos² A - 4 cos A = 0

cos A (5 cos A - 4) = 0, cos A ≠ 0

5 cos A - 4 = 0

cos A = 4 / 5

sec A - tan A = 5 / 4 - 3 / 4 = 2 / 4 = 1 / 2 (correct)