What is the general solution for sin(θ)=sqrt(1+(1-(cos(θ)-1)^2)) ?

The general solution for sin(θ)=sqrt(1+(1-(cos(θ)-1)^2)) is θ= pi/2+2pin

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sin(θ)=sqrt(1+(1-(cos(θ)-1)^2))

sin (θ) = 1 + (1 - (cos (θ) - 1)^{2})

θ = \frac{π}{2} + 2 πn

Solution steps

sin (θ) = 1 + (1 - (cos (θ) - 1)^{2})

Square both sides

sin^{2} (θ) = (1 + 1 - (cos (θ) - 1)^{2})^{2}

Subtract

1 + 1 - (cos (θ) - 1)^{2}^{2}

from both sides

sin^{2} (θ) - 2 cos (θ) + cos^{2} (θ) - 1 = 0

Rewrite using trig identities

- 1 - 2 cos (θ) + 1 = 0

Group like terms

- 2 cos (θ) - 1 + 1 = 0

- 1 + 1 = 0

- 2 cos (θ) = 0

Divide both sides by

- 2

cos (θ) = 0

General solutions for

cos (θ) = 0

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Verify solutions by plugging them into the original equation

θ = \frac{π}{2} + 2 πn

0 = 4 cos (4 x)

tan (θ) = \frac{8}{7}, π < θ < \frac{3 π}{2}

csc (θ) sin (θ) = cot (θ)

7 sin (θ) + cos (θ) = 5

tan (θ + π) + 2 sin (θ + π) = 0

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