Question

2sin^2 A + 5cosA = 4 , Prove that cos A = 1/2

Answer 1

2sin^2 A + 5cosA = 4
2(1 - cos^2 A) + 5cosA - 4 = 0
2cos^2 A - 5cosA + 2 = 0
(2cosA -1)(cosA - 2) = 0
cosA = 1/2 or cosA = -2, the latter is not possible,

so cosA = 1/2