2cos^2(x/2)=1

Solución

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

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

Pasos de solución

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

Usando el método de sustitución

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

cos (\frac{x}{2}) = \frac{1}{2} : x = \frac{π}{2} + 4 πn, x = 4 π - \frac{π}{2} + 4 πn

cos (\frac{x}{2}) = - \frac{1}{2} : x = \frac{3 π}{2} + 4 πn, x = - \frac{3 π}{2} + 4 πn

Combinar toda las soluciones

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

sin^{2} (θ) = 2 cos (θ) + 2

cos (4 x) (cos (x) - 1) = 0

3 tan (\frac{x}{2}) + 3 = 0

4 cos (x) tan (x) = 5 tan (x)

4 cos^{2} (2 x) - 1 = 0