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

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

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cos^2(x)-sin^2(x)= 1/2

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

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

Solution steps

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

Rewrite using trig identities

cos (2 x) = \frac{1}{2}

General solutions for

cos (2 x) = \frac{1}{2}

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

Solve

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

Solve

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

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

2 cos^{2} (θ) - cos (θ) = 0

3 tan^{2} (θ) - 1 = 0

sin (2 θ - \frac{π}{2}) = - 1

sin (\frac{x}{2}) + cos (x) = 0

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

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