writing the expression for one variable in terms of another

Assuming[Element[C[1], Integers], h[x] == 0 /. sol // Simplify] (* {True, True} *) The first solution is all even multiples of Pi. The second solution is all odd multiples of Pi.

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Manipulating Equations and Inequalities

Solve finds what are known as generic solutions to equations. These are solutions that do not depend on the variables not specified in the second argument. For example: No matter what y
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