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/3+pin,x=(2pi)/3+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}{3} + πn, x = \frac{2 π}{3} + 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{2 π}{3} + 2 πn, 2 x = \frac{4 π}{3} + 2 πn

Solve

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

Solve

2 x = \frac{4 π}{3} + 2 πn : x = \frac{2 π}{3} + πn

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

cos (θ) + 2 cos (θ + 24 0^{\circ}) = 1

arccos (x) = \frac{π}{8}

sin (θ) = 5

sin^{2} (x) = 4 cos (x)

- 8 cos (x) sin (x) = 0

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/3+pin,x=(2pi)/3+pin