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

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

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2-sin(x)=sin(x)

2 - sin (x) = sin (x)

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

2 - sin (x) = sin (x)

Solve by substitution

2 - sin (x) = sin (x)

Let:

sin (x) = u

2 - u = u

2 - u = u : u = 1

2 - u = u

Move

2

to the right side

2 - u = u

Subtract

2

from both sides

2 - u - 2 = u - 2

Simplify

- u = u - 2

- u = u - 2

Move

u

to the left side

- u = u - 2

Subtract

u

from both sides

- u - u = u - 2 - u

Simplify

- 2 u = - 2

- 2 u = - 2

Divide both sides by

- 2

- 2 u = - 2

Divide both sides by

- 2

\frac{- 2 u}{- 2} = \frac{- 2}{- 2}

Simplify

u = 1

u = 1

Substitute back

u = sin (x)

sin (x) = 1

sin (x) = 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 1

General solutions for

sin (x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

cos^{2} (t) = \frac{1}{2}

2 cos^{2} (θ) - 1 = sin (θ), 0^{\circ} \leq θ \leq 18 0^{\circ}

x, e^{c o s (x)} (1 - cos (y)) = c

22 = 2 sec (θ)

cos^{4} (x) - sin^{4} (x) = \frac{1}{2}

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