Question

The angle A is such that

secA + tanA = 2
Show that
secA-tanA=1/2
Hence, find the exact value of cosA.

Answer 1

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 )