Solve the equation `(sin 3x)/2+(cos 3x)/2=sqrt 5`

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The equation `(sin3x)/2+(cos3x)/2=sqrt 5` has to be solved

`(sin3x)/2+(cos3x)/2=sqrt 5`

=> `sin3x+cos3x = 2*sqrt 5`

=> `sin^2 3x + cos^2 3x + 2*sin 3x*cos 3x = 4*5`

=> `1 + sin 6x = 20`

=> `sin 6x = 19`

This is not possible as sin 6x lies in [-1, 1]

The given equation does not have any solutions

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