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

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

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

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

x = 2 πn

Solution steps

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

Subtract

cos (x) - 1

from both sides

sin^{2} (\frac{x}{2}) - cos (x) + 1 = 0

Rewrite using trig identities

1 + \frac{1 - 3 cos ( x )}{2} = 0

Move

1

to the right side

\frac{1 - 3 cos ( x )}{2} = - 1

Multiply both sides by

2

1 - 3 cos (x) = - 2

Move

1

to the right side

- 3 cos (x) = - 3

Divide both sides by

- 3

cos (x) = 1

General solutions for

cos (x) = 1

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn

sin (x) = cos (2 x), 0 \leq x \leq 2 π

sin (2 x) = sin (x) cos (x)

sin (θ) = - \frac{5}{5}, \frac{3 π}{2} < θ < 2 π

(2 sin (2 x) - 1) (3 tan (2 x) - 1) = 0

- 0.2588 + 0.9659 tan (b) = 1.4201

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