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

The general solution for cos^2(x)-sin^2(x)=(sqrt(3))/2 is x= pi/(12)+pin,x=(11pi)/(12)+pin

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

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

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

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

Rewrite using trig identities

cos (2 x) = \frac{3}{2}

General solutions for

cos (2 x) = \frac{3}{2}

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

2 sin^{2} (x) + 1 = 4 sin (x)

\frac{1}{4} = cos (x)

cos (2 x) + 3 cos (x) = - 2

4 tan^{2} (θ) + 16 tan (θ) = 7 tan (θ) - 2

10 (1 - cos (θ)) = sin^{2} (θ)

What is the general solution for cos^2(x)-sin^2(x)=(sqrt(3))/2 ?
The general solution for cos^2(x)-sin^2(x)=(sqrt(3))/2 is x= pi/(12)+pin,x=(11pi)/(12)+pin