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

The general solution for cos^2(θ)-sin^2(θ)= 1/2 is θ= pi/6+pin,θ=(5pi)/6+pin

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cos^2(θ)-sin^2(θ)= 1/2

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

θ = \frac{π}{6} + πn, θ = \frac{5 π}{6} + πn

Solution steps

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

Rewrite using trig identities

cos (2 θ) = \frac{1}{2}

General solutions for

cos (2 θ) = \frac{1}{2}

2 θ = \frac{π}{3} + 2 πn, 2 θ = \frac{5 π}{3} + 2 πn

Solve

2 θ = \frac{π}{3} + 2 πn : θ = \frac{π}{6} + πn

Solve

2 θ = \frac{5 π}{3} + 2 πn : θ = \frac{5 π}{6} + πn

θ = \frac{π}{6} + πn, θ = \frac{5 π}{6} + πn

tan (\frac{x}{9}) = 1

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

3 + sin (3 x) = 2

2 sin (x) - sin (2 x) = 0

sin (2 θ) = - 3 cos (2 θ)

What is the general solution for cos^2(θ)-sin^2(θ)= 1/2 ?
The general solution for cos^2(θ)-sin^2(θ)= 1/2 is θ= pi/6+pin,θ=(5pi)/6+pin