What is the general solution for 1-cos^2(θ)+sqrt(3)=2sin(θ)+sqrt(3) ?

The general solution for 1-cos^2(θ)+sqrt(3)=2sin(θ)+sqrt(3) is θ=2pin,θ=pi+2pin

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1-cos^2(θ)+sqrt(3)=2sin(θ)+sqrt(3)

1 - cos^{2} (θ) + 3 = 2 sin (θ) + 3

θ = 2 πn, θ = π + 2 πn

Solution steps

1 - cos^{2} (θ) + 3 = 2 sin (θ) + 3

Subtract

2 sin (θ) + 3

from both sides

- cos^{2} (θ) - 2 sin (θ) + 1 = 0

Rewrite using trig identities

sin^{2} (θ) - 2 sin (θ) = 0

Solve by substitution

sin (θ) = 2, sin (θ) = 0

sin (θ) = 2 :

No Solution

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

sin (4 θ) = sin (2 θ)

y, x sin (y) = x

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

2 tan^{2} (x) = - 3 + 3 sec (x)

5 csc^{2} (\frac{θ}{2}) - 16 = 0

What is the general solution for 1-cos^2(θ)+sqrt(3)=2sin(θ)+sqrt(3) ?
The general solution for 1-cos^2(θ)+sqrt(3)=2sin(θ)+sqrt(3) is θ=2pin,θ=pi+2pin