What is the general solution for cos^2(x/3)-sin^2(x/3)=-1/2 ?

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

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cos^2(x/3)-sin^2(x/3)=-1/2

cos^{2} (\frac{x}{3}) - sin^{2} (\frac{x}{3}) = - \frac{1}{2}

x = π + 3 πn, x = 2 π + 3 πn

Solution steps

cos^{2} (\frac{x}{3}) - sin^{2} (\frac{x}{3}) = - \frac{1}{2}

Rewrite using trig identities

cos (2 \cdot \frac{x}{3}) = - \frac{1}{2}

General solutions for

cos (2 \cdot \frac{x}{3}) = - \frac{1}{2}

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

Solve

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

Solve

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

x = π + 3 πn, x = 2 π + 3 πn

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6 cos (2 x) + 8 sin (2 x) = 0

cos (x) = \frac{8}{17}, sin (x)

\frac{50}{sin ( 10 5 ^{\circ} )} = \frac{20}{sin ( x )}

x, sin^{2} (x) = \frac{5 m - 5}{2}

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