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

The general solution for 1-sin(θ)=2cos^2(θ) is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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1-sin(θ)=2cos^2(θ)

1 - sin (θ) = 2 cos^{2} (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

1 - sin (θ) = 2 cos^{2} (θ)

Subtract

2 cos^{2} (θ)

from both sides

1 - sin (θ) - 2 cos^{2} (θ) = 0

Rewrite using trig identities

- 1 - sin (θ) + 2 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{1}{2}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

2 sin^{2} (θ) - 3 sin (θ) = 0

sec^{2} (x) + 2 tan (x) = 4

tan (\frac{x}{5}) + 3 = 0

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

2 sin (x + \frac{π}{2}) + 3 tan (π - x) = 0

What is the general solution for 1-sin(θ)=2cos^2(θ) ?
The general solution for 1-sin(θ)=2cos^2(θ) is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin