Question

Find A, if 0° ≤ A ≤ 90° and : 2cos² A + cos A - 1 = 0
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Answer 1

2cos²A+cosA-1=0
using factorisation method,
2cos²A+2cosA-cosA-1=0
Taking common factor,
2cosA(cosA+1)-1(cosA+1)=0
(2cosA-1)(cosA+1)=0
cosA+1=0
cosA=-1
cosA=cos180
A=180 degrees      (not possible as A<90)

2cosA-1=0
2cosA=1
cosA=1/2
cosA=cos45
A=45 degrees
 

Angle A is 45 degrees