SOLUTION: Solve 2sinxtanx=5-(1/cosx)

Question 1081140: Solve 2sinxtanx=5-(1/cosx)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2 sin x*(sin x/ cos x)=(5 cos x-1)/cos x
2 sin ^2 x=5 cos x-1
2(1-cos^2)x=5 cos x-1
2-2 cos^2 x=5 cos x -1
0=2cos^2x+5 cos x -3= (2 cos x-1)(cos x +3)=0
only one of those factors works, and it is when cos x=1/2
That is at pi/3 and 5 pi/3
Check
2*(sqrt(3)/2)* sqrt (3)=5-(1/(1/2))
3=3

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