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

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

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

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

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

Solution steps

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

Subtract

- sin (x)

from both sides

1 - cos (x) + sin (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{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

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

Solve

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

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

tan (x) = 1, - 2 π \leq x \leq 2 π

(- 4 cos (x) - 6 sin (x))^{2} - 20 sin^{2} (x) = 16

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

3 cot^{2} (2 t - \frac{3 π}{2}) = 1

3 cot (θ) - 2 = 0

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