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

The general solution for -pi/2 =1-2sin(x) is No Solution for x\in\mathbb{R}

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-pi/2 =1-2sin(x)

- \frac{π}{2} = 1 - 2 sin (x)

No Solution for x \in R

Solution steps

- \frac{π}{2} = 1 - 2 sin (x)

Switch sides

1 - 2 sin (x) = - \frac{π}{2}

Move

1

to the right side

1 - 2 sin (x) = - \frac{π}{2}

Subtract

1

from both sides

1 - 2 sin (x) - 1 = - \frac{π}{2} - 1

Simplify

- 2 sin (x) = - \frac{π}{2} - 1

- 2 sin (x) = - \frac{π}{2} - 1

Divide both sides by

- 2

- 2 sin (x) = - \frac{π}{2} - 1

Divide both sides by

- 2

\frac{- 2 sin ( x )}{- 2} = - \frac{\frac{π}{2}}{- 2} - \frac{1}{- 2}

Simplify

\frac{- 2 sin ( x )}{- 2} = - \frac{\frac{π}{2}}{- 2} - \frac{1}{- 2}

Simplify

\frac{- 2 sin ( x )}{- 2} : sin (x)

\frac{- 2 sin ( x )}{- 2}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 sin ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (x)

Simplify

- \frac{\frac{π}{2}}{- 2} - \frac{1}{- 2} : \frac{π + 2}{4}

- \frac{\frac{π}{2}}{- 2} - \frac{1}{- 2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- \frac{π}{2} - 1}{- 2}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

- \frac{π}{2} - 1 = - (\frac{π}{2} + 1)

= \frac{\frac{π}{2} + 1}{2}

Join

\frac{π}{2} + 1 : \frac{π + 2}{2}

\frac{π}{2} + 1

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

= \frac{π}{2} + \frac{1 \cdot 2}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π + 1 \cdot 2}{2}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{π + 2}{2}

= \frac{\frac{π + 2}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π + 2}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π + 2}{4}

sin (x) = \frac{π + 2}{4}

sin (x) = \frac{π + 2}{4}

sin (x) = \frac{π + 2}{4}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

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What is the general solution for -pi/2 =1-2sin(x) ?
The general solution for -pi/2 =1-2sin(x) is No Solution for x\in\mathbb{R}