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

Solución

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

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

Pasos de solución

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

Restar

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

de ambos lados

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

Simplificar

cos^{2} (x) - \frac{1 - cos ( 2 x )}{2} : \frac{2 cos ^{2} ( x ) - 1 + cos ( 2 x )}{2}

\frac{2 cos ^{2} ( x ) - 1 + cos ( 2 x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Re-escribir usando identidades trigonométricas

2 cos^{2} (x) - 2 sin^{2} (x) = 0

Factorizar

2 cos^{2} (x) - 2 sin^{2} (x) : 2 (cos (x) + sin (x)) (cos (x) - sin (x))

2 (cos (x) + sin (x)) (cos (x) - sin (x)) = 0

Resolver cada parte por separado

cos (x) + sin (x) = 0 or cos (x) - sin (x) = 0

cos (x) + sin (x) = 0 : x = \frac{3 π}{4} + πn

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

Combinar toda las soluciones

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

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

- 9 sin (3 x) = 0

cos (4 x) - 7 cos (2 x) = 8

6 tan (B) + 14 = 0

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4