What is x in sin x +cosx =0?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`sinx+cosx = 0`

`sinx = -cosx`

`sinx = sin(pi/2+x)`

`x = npi+(-1)^n(pi/2+x)`

`x(1-(-1)^n) = npi+(-1)^n(pi)/2`

`x = (npi+(-1)^n(pi)/2)/(1-(-1)^n)`

So the answer is `x = (npi+(-1)^n(pi)/2)/(1-(-1)^n).`

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