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}

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

y, z = e^{x} sin (x y)

5 sin^{2} (θ) + 11 sin (θ) + 6 = 0

cot^{2} (x) - 4 cot (x) + 3 = 0

2 cos (x) + 1 = sec (x)

2 sin (θ) = 1, 0 \leq θ \leq 2 π

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