What is the general solution for sin(x)-1=-cos(2x) ?

The general solution for sin(x)-1=-cos(2x) is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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sin(x)-1=-cos(2x)

sin (x) - 1 = - cos (2 x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

sin (x) - 1 = - cos (2 x)

Subtract

- cos (2 x)

from both sides

sin (x) - 1 + cos (2 x) = 0

Rewrite using trig identities

sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = \frac{1}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 cos (\frac{x}{2}) - 2 = 0, 0 \leq x < 2 π

cos (\frac{x}{4}) = - \frac{2}{2}

tan (θ) = \frac{- 4}{4}

tan (x) = \frac{12}{20}

2 sin (x) + sin (x) = 0

What is the general solution for sin(x)-1=-cos(2x) ?
The general solution for sin(x)-1=-cos(2x) is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin