# Math Scene

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

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

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

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

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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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