Question

Solve the equations `sin^2x=2sinx` and `2cos^2x-4cosx=0`?

Answer 1

Solve each equation separately, then attempt to extract only the common solutions.
In this case no solutions are possible.

Explanation:

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In this case there are no common values for `x`, so the equations are incompatible.

Note: since both `sin(x)` and `cos(x)` must be in the range `[-1,+1]`,
neither `sin(x)-2` nor `2cos(x)-4` can be zero and hence we can divide by them to get `sinx=0` and `cosx=0`.