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

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

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

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

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

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

Subtract

- 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 = 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}

36 cos (2 x) = 0

2 sin^{2} (θ) + sin (θ) = 0, 0 \leq θ < 2 π

sin (x) + cos (x) = 0, - π \leq x \leq π

cos (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

2 + 4 cos (θ) = 0

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