What is the general solution for (sin(x)+cos(x))^2=1 ?

The general solution for (sin(x)+cos(x))^2=1 is x=2pin+pi,x=2pin+(3pi)/2 ,x=2pin,x=2pin+pi/2

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(sin(x)+cos(x))^2=1

(sin (x) + cos (x))^{2} = 1

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}, x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

(sin (x) + cos (x))^{2} = 1

Subtract

1

from both sides

(sin (x) + cos (x))^{2} - 1 = 0

Factor

(sin (x) + cos (x))^{2} - 1 : (sin (x) + cos (x) + 1) (sin (x) + cos (x) - 1)

(sin (x) + cos (x) + 1) (sin (x) + cos (x) - 1) = 0

Solving each part separately

sin (x) + cos (x) + 1 = 0 or sin (x) + cos (x) - 1 = 0

sin (x) + cos (x) + 1 = 0 : x = 2 πn + π, x = 2 πn + \frac{3 π}{2}

sin (x) + cos (x) - 1 = 0 : x = 2 πn, x = 2 πn + \frac{π}{2}

Combine all the solutions

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}, x = 2 πn, x = 2 πn + \frac{π}{2}

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What is the general solution for (sin(x)+cos(x))^2=1 ?
The general solution for (sin(x)+cos(x))^2=1 is x=2pin+pi,x=2pin+(3pi)/2 ,x=2pin,x=2pin+pi/2