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How to further simplify and combine solution sets of trigonometric equations?

Posted 2 days ago

When solving the following trigonometric equation, the solution set obtained is:

Solve[{5 (Sin[5 x + \[Phi]] - Sin[x]) == 0, 
  0 <= \[Phi] <= 2 \[Pi]}, x, Reals]

enter image description here

How to further simplify and combine solution sets of trigonometric equations to obtain the following solution form?

{{x -> ConditionalExpression[
    1/6 (\[Pi] - \[Phi] + 
       2 \[Pi] ConditionalExpression[1, \[Placeholder]]), 
    ConditionalExpression[1, \[Placeholder]] \[Element] Integers && 
     0 <= \[Phi] <= 2 \[Pi]]}, {x -> 
   ConditionalExpression[
    1/4 (-\[Phi] + 2 \[Pi] ConditionalExpression[1, \[Placeholder]]), 
    ConditionalExpression[1, \[Placeholder]] \[Element] Integers && 
     0 <= \[Phi] <= 2 \[Pi]]}}

enter image description here

POSTED BY: Bill Blair
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