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

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

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sin(x)=1+cos(x)

sin (x) = 1 + cos (x)

x = \frac{π}{2} + 2 πn, x = 2 πn + π

Solution steps

sin (x) = 1 + cos (x)

Subtract

1 + cos (x)

from both sides

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

Rewrite using trig identities

- 1 + 2 sin (x - \frac{π}{4}) = 0

Move

1

to the right side

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 = \frac{π}{2} + 2 πn

Solve

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

x = \frac{π}{2} + 2 πn, x = 2 πn + π

2 sin (x) = 1 + \frac{cos ( 2 x )}{sin ( x )}

sin (x) = \frac{21}{5}

tan (\frac{θ}{2} - \frac{π}{6}) = 1

1 + 2 sin (θ) = csc (θ)

- 6 = - 4 + sec (x + \frac{π}{4})

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