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solvefor x,sin^2(x)+cos^2(y)=1

Solución

resolver para

x, sin^{2} (x) + cos^{2} (y) = 1

x = arcsin (- sin (y)) + 2 πn, x = π + arcsin (sin (y)) + 2 πn, x = arcsin (sin (y)) + 2 πn, x = π + arcsin (- sin (y)) + 2 πn

Pasos de solución

sin^{2} (x) + cos^{2} (y) = 1

Restar

1

de ambos lados

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

Re-escribir usando identidades trigonométricas

- 1 + cos^{2} (y) + sin^{2} (x)

Utilizar la identidad pitagórica:

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

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

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

- sin^{2} (y) + sin^{2} (x) = 0

Factorizar

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

- sin^{2} (y) + sin^{2} (x)

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

sin^{2} (x) - sin^{2} (y) = (sin (x) + sin (y)) (sin (x) - sin (y))

= (sin (x) + sin (y)) (sin (x) - sin (y))

(sin (x) + sin (y)) (sin (x) - sin (y)) = 0

Resolver cada parte por separado

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

sin (x) + sin (y) = 0 : x = arcsin (- sin (y)) + 2 πn, x = π + arcsin (sin (y)) + 2 πn

sin (x) + sin (y) = 0

Mover

sin (y)

al lado derecho

sin (x) + sin (y) = 0

Restar

sin (y)

de ambos lados

sin (x) + sin (y) - sin (y) = 0 - sin (y)

Simplificar

sin (x) = - sin (y)

sin (x) = - sin (y)

Aplicar propiedades trigonométricas inversas

sin (x) = - sin (y)

Soluciones generales para

sin (x) = - sin (y)

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- sin (y)) + 2 πn, x = π + arcsin (sin (y)) + 2 πn

x = arcsin (- sin (y)) + 2 πn, x = π + arcsin (sin (y)) + 2 πn

sin (x) - sin (y) = 0 : x = arcsin (sin (y)) + 2 πn, x = π + arcsin (- sin (y)) + 2 πn

sin (x) - sin (y) = 0

Mover

sin (y)

al lado derecho

sin (x) - sin (y) = 0

Sumar

sin (y)

a ambos lados

sin (x) - sin (y) + sin (y) = 0 + sin (y)

Simplificar

sin (x) = sin (y)

sin (x) = sin (y)

Aplicar propiedades trigonométricas inversas

sin (x) = sin (y)

Soluciones generales para

sin (x) = sin (y)

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (sin (y)) + 2 πn, x = π + arcsin (- sin (y)) + 2 πn

x = arcsin (sin (y)) + 2 πn, x = π + arcsin (- sin (y)) + 2 πn

Combinar toda las soluciones

x = arcsin (- sin (y)) + 2 πn, x = π + arcsin (sin (y)) + 2 πn, x = arcsin (sin (y)) + 2 πn, x = π + arcsin (- sin (y)) + 2 πn

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

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

tan (x) = \frac{3}{10}

y = 1 + sin (\frac{π x}{4}), x

sec (\frac{x}{2}) = 2