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(1+tan^2(x))/(1+tan^2(x))=1-sin^2(x)

Solución

\frac{1 + tan ^{2} ( x )}{1 + tan ^{2} ( x )} = 1 - sin^{2} (x)

Solución

x = 2 πn, x = π + 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{1 + tan ^{2} ( x )}{1 + tan ^{2} ( x )} = 1 - sin^{2} (x)

\frac{1 + tan ^{2} ( x )}{1 + tan ^{2} ( x )} = 1

\frac{1 + tan ^{2} ( x )}{1 + tan ^{2} ( x )}

Aplicar la regla

\frac{a}{a} = 1

= 1

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

Intercambiar lados

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

Mover

1

al lado derecho

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

Restar

1

de ambos lados

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

Simplificar

- sin^{2} (x) = 0

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

- sin^{2} (x) = 0

Dividir ambos lados entre

- 1

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

Simplificar

sin^{2} (x) = 0

sin^{2} (x) = 0

Aplicar la regla

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

sin (x) = 0

Soluciones generales para

sin (x) = 0

tabla de valores periódicos con

2 πn

intervalos:

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 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, x = π + 2 πn

Ejemplos populares

solvefor θ,tan(θ)=(2sqrt(3))/2 resolver para

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(-3+4cos^2(θ))/(1-2sin(θ))=a+bsin(θ)

\frac{- 3 + 4 cos ^{2} ( θ )}{1 - 2 sin ( θ )} = a + b sin (θ)

2sin^2(x)-7sin(x)=-3,0<= x<= 2pi

2 sin^{2} (x) - 7 sin (x) = - 3, 0 \leq x \leq 2 π

sin^2(x)+cos^2(x)=cos(2x)

sin^{2} (x) + cos^{2} (x) = cos (2 x)

(218)sin^2(x)+(126)sin(x)-88=0

(218) sin^{2} (x) + (126) sin (x) - 88 = 0