4sinA=5cos2A+1
4sinA=5(cos^2 A-sin^2 A)+1
5sin^2 A+4sinA-1-5cos^2 A=0
5sin^2 A+4sinA-1-(5-5sin^2 A)=0
10sin^2 A+4sinA-6=0
5sin^2 A+2sinA-3=0
(5sinA-3)(sinA+1)=0
所以sinA=3/5
因为A属于(90度,180度),
所以cosA=-4/5