The equation "sin (x) + cos (x) = 0" has only one solution set "$x=frac3pi 4+pi n$".

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Why it has not solution mix "$x=frac7pi 4+pi n$"? Although it satisfy the equation.

Please help quickly.


The equation is equivalent to$$ an x=-1$$ since the two functions $cos$ & $sin$ don"t vanish together so we find$$xequivfrac3pi4mod pi$$

A solution phối is a set of points that satisfies a given equation. A given equation will have only one solution set. That phối can have many descriptions. $frac 3pi4+npi$ is one description of the solution mix for this equation. $frac 7pi4+mpi$ is another description of the same set.


Note that$$frac7pi4 + npi = left(1 + frac34 ight)pi + npi = frac3pi4 + (n+1)pi,$$so you are naming the same mix of solutions but with a different indexing system.


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