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

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

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1=sin(x)+cos(x)

1 = sin (x) + cos (x)

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

1 = sin (x) + cos (x)

Switch sides

sin (x) + cos (x) = 1

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

x + \frac{π}{4} = \frac{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{4} + 2 πn : x = 2 πn

Solve

x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{2}

x = 2 πn, x = 2 πn + \frac{π}{2}

cos (2 t) - cos (t) = - 0.5, 0 < t < 2 π

2 sin (x) - sin (x) cos (x) = 0

3 sin (x) - 2 cos (x) = 7

cos (x) = 0.6345

cos (t) = \frac{40}{41}

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