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tan^2(x)cos(x)=tan^2(x)

Solução

tan^{2} (x) cos (x) = tan^{2} (x)

x = πn

Graus

x = 0^{\circ} + 18 0^{\circ} n

Passos da solução

tan^{2} (x) cos (x) = tan^{2} (x)

Subtrair

tan^{2} (x)

de ambos os lados

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

Fatorar

tan^{2} (x) cos (x) - tan^{2} (x) : tan^{2} (x) (cos (x) - 1)

tan^{2} (x) cos (x) - tan^{2} (x)

Fatorar o termo comum

tan^{2} (x)

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

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

Resolver cada parte separadamente

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

tan^{2} (x) = 0 : x = πn

tan^{2} (x) = 0

Aplicar a regra

x^{n} = 0 \Rightarrow x = 0

tan (x) = 0

Soluções gerais para

tan (x) = 0

tan (x)

tabela de periodicidade com ciclo de

πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Resolver

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 0

Mova

1

para o lado direito

cos (x) - 1 = 0

Adicionar

1

a ambos os lados

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

Simplificar

cos (x) = 1

cos (x) = 1

Soluções gerais para

cos (x) = 1

cos (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Combinar toda as soluções

x = πn, x = 2 πn

Junte intervalos que se sobrepoem

x = πn