(1+tan^2(27θ))/(1-tan^2(27θ))=sqrt(2)

Solución

\frac{1 + tan ^{2} ( 27 \cdot θ )}{1 - tan ^{2} ( 27 \cdot θ )} = 2

θ = \frac{0.39269 \dots}{27} + \frac{πn}{27}, θ = \frac{- 0.39269 \dots}{27} + \frac{πn}{27}

Pasos de solución

\frac{1 + tan ^{2} ( 27 θ )}{1 - tan ^{2} ( 27 θ )} = 2

Usando el método de sustitución

tan (27 θ) = 2 - 1, tan (27 θ) = - 2 + 1

tan (27 θ) = 2 - 1 : θ = \frac{arctan ( 2 - 1 )}{27} + \frac{πn}{27}

tan (27 θ) = - 2 + 1 : θ = \frac{arctan ( - 2 + 1 )}{27} + \frac{πn}{27}

Combinar toda las soluciones

θ = \frac{arctan ( 2 - 1 )}{27} + \frac{πn}{27}, θ = \frac{arctan ( - 2 + 1 )}{27} + \frac{πn}{27}

Mostrar soluciones en forma decimal

θ = \frac{0.39269 \dots}{27} + \frac{πn}{27}, θ = \frac{- 0.39269 \dots}{27} + \frac{πn}{27}

tan (x) = - cot (x)

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

cos (x) = - 0.6

cos (x) = - 0.9

2 cos (x) + 3 sin (x) = 0