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

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

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cos(x)=1+sin(x)

cos (x) = 1 + sin (x)

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

Solution steps

cos (x) = 1 + sin (x)

Subtract

1 + sin (x)

from both sides

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

Rewrite using trig identities

- 1 - 2 sin (\frac{4 x - π}{4}) = 0

Move

1

to the right side

- 2 sin (\frac{4 x - π}{4}) = 1

Divide both sides by

- 2

sin (\frac{4 x - π}{4}) = - \frac{2}{2}

General solutions for

sin (\frac{4 x - π}{4}) = - \frac{2}{2}

\frac{4 x - π}{4} = \frac{5 π}{4} + 2 πn, \frac{4 x - π}{4} = \frac{7 π}{4} + 2 πn

Solve

\frac{4 x - π}{4} = \frac{5 π}{4} + 2 πn : x = \frac{3 π}{2} + 2 πn

Solve

\frac{4 x - π}{4} = \frac{7 π}{4} + 2 πn : x = 2 π + 2 πn

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

(tan (x) + 3) (cos (x) + 2) = 0

x, cos (y) + sin (x) = 1

cot (x) + 5 csc (x) = 6

csc^{2} (x) = 1

1 - cos (x) = \frac{1}{2}

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