If cosx-2cos2x=0 then x=?
ananya071:
That is cos square x or twice of x
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cos2x = 2cos²x -1
Substitute this in the question,
cosx - 2cos2x =0
cosx -2(2cos²x -1)=0
-4cos²x +cosx +2=0
4cos²x -cosx -2=0
let cosx = y, then,
4y² -y -2=0
Discriminant = b²-4ac = 1 - 4×4×(-2) = 33
y = (-b±√D)/2a
y = (1±√33)/8
x = cos inverse {(1±√33)/8}
Substitute this in the question,
cosx - 2cos2x =0
cosx -2(2cos²x -1)=0
-4cos²x +cosx +2=0
4cos²x -cosx -2=0
let cosx = y, then,
4y² -y -2=0
Discriminant = b²-4ac = 1 - 4×4×(-2) = 33
y = (-b±√D)/2a
y = (1±√33)/8
x = cos inverse {(1±√33)/8}
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