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

The general solution for sin^2(x)-cos^2(x)= 1/2 is x= pi/3+pin,x=(2pi)/3+pin

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

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

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

- 1

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

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

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

sec (4 x) - 2 = 0

2 cos (θ) sin (θ) = cos (θ)

- 2 sin (x) = 0

What is the general solution for sin^2(x)-cos^2(x)= 1/2 ?
The general solution for sin^2(x)-cos^2(x)= 1/2 is x= pi/3+pin,x=(2pi)/3+pin