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

The general solution for 2(cos^2(x)-sin^2(x))=1 is x= pi/6+pin,x=(5pi)/6+pin

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

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

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

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

Rewrite using trig identities

2 cos (2 x) = 1

Divide both sides by

2

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

General solutions for

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

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

- sin (θ) + cos (2 θ) = 1

arctan (2 x - 8) = - 1

- 2 cos (2 θ) - 5 = - 4 sin (θ) - 8

3 cos^{2} (θ) - cos (θ) = 0

10 sin^{2} (x) + 11 sin (x) - 8 = 0

What is the general solution for 2(cos^2(x)-sin^2(x))=1 ?
The general solution for 2(cos^2(x)-sin^2(x))=1 is x= pi/6+pin,x=(5pi)/6+pin