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

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

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cos(2θ)-sin^2(θ)=1

cos (2 θ) - sin^{2} (θ) = 1

θ = 2 πn, θ = π + 2 πn

Solution steps

cos (2 θ) - sin^{2} (θ) = 1

Subtract

1

from both sides

cos (2 θ) - sin^{2} (θ) - 1 = 0

Rewrite using trig identities

- 3 sin^{2} (θ) = 0

Divide both sides by

- 3

sin (θ) = 0

General solutions for

sin (θ) = 0

θ = 0 + 2 πn, θ = π + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 2 πn, θ = π + 2 πn

sin (x) = \frac{3}{4}

2 sin (2 x) = 3 sin (x)

4 sin (\frac{t}{2}) - 1 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

- 6 cos (θ) - 10 = - 7

sin^{2} (x) = cos^{2} (x) + 1

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