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La solución del problema es : x = (sin ^ - 1( - 2 / m) + 2πn) / 2, x = (π + sin ^ - 1( - 2 / m) + 2πn) / 2Siendo ; m = <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x-307%5Cpi%20%29csc%28x-%5Cfrac%7B905%5Cpi%20%7D%7B2%7D%20%29%7D%7Bsin%28x-%5Cfrac%7B307%5Cpi%20%7D%7B2%7D%29sin%28x-905%5Cpi%20%29%20%7D" />cos(x - 307π) Usando la identidad : cos(s - t) = cos(s)cos(t) + sin(s)sin(t) = cos(x)cos(307π) + sin(x)sin(307π)Simplificar ; cos(x)cos(307π) Evaluar ; cos(307π) = - 1 = ( - 1)cos(x)cos(x)cos(307π) = - cos(x)sin(x)sin(307π)Evaluar ; sin(307π) = 0 = (0)cos(x)sin(x)sin(307π) = 0Sustituimos ; = - cos(x) + 0cos(x)cos(307π) + sin(x)sin(307π) = - cos(x)sin(x - 905π)Usando la identidad : sin(s - t) = - cos(s)sin(t) + sin(s)cos(t) = - cos(x)sin(905π) + sin(x)cos(905π)Simplificar ; cos(x)sin(905π)Evaluamos ; sin(905π) = 0 = (0)cos(x)cos(x)sin(905π) = 0sin(x)cos(905π)Evaluamos ; cos(905π) = - 1 = ( - 1)sin(x)sin(x)cos(905π) = - sin(x)Sustituimos ; - cos(x)sin(905π) + sin(x)cos(905π) = - 0 - sin(x) - cos(x)sin(905π) + sin(x)cos(905π) = sin(x)csc(x - 905π / 2)Usamos la identidad : csc(x) = 1 / sin(x) = 1 / sin( - 905π / 2 + x)Usamos la identidad : sin(s - t) = - cos(s)sin(t) + sin(s)cos(t) = 1 / - cos(x)sin(905π / 2) + sin(x)cos(905π / 2)Simplificar ; - cos(x)sin(905π / 2) + sin(x)cos(905π / 2)cos(x)sin(905π / 2)Evaluamos ; sin(905π / 2) = 1 cos(x)sin(905π / 2) = cos(x)sin(x)cos(905π / 2)Evaluamos ; cos(905π / 2) = 0 = 0 sin(x)sin(x)cos(905π / 2) = 0Sustituimos ; - cos(x)sin(905π / 2) + sin(x)cos(905π / 2) = - cos(x)1 / - cos(x)sin(905π / 2) + sin(x)cos(905π / 2) = - 1 / cos(x)sin(x - 307π / 2)Usamos la identidad : sin(s - t) = - cos(s)sin(t) + sin(s)cos(t) = - cos(x)sin(307π / 2) + sin(x)cos(307π / 2)Simplificamos ; cos(x)sin(307π / 2)Evaluamos ; sin(307π / 2) = - 1 = ( - 1)cos(x)cos(x)sin(307π / 2) = - cos(x)sin(x)cos(307π / 2)Evaluamos ; cos(307π / 2) = 0 = (0)sin(x)sin(x)cos(307π / 2) = 0Sustituimos ; = - ( - cos(x)) + 0 - cos(x)sin(307π / 2) + sin(x)cos(307π / 2) = cos(x)Sustituimos ; m = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B-cos%28x%29%28-%5Cfrac%7B1%7D%7Bcos%28x%29%7D%29%20%7D%7Bcos%28x%29%28-sin%28x%29%29%7D" />Simplificar ; <img src="https://tex.z-dn.net/?f=%5Cfrac%7B-cos%28x%29%28-%5Cfrac%7B1%7D%7Bcos%28x%29%7D%29%20%7D%7Bcos%28x%29%28-sin%28x%29%29%7D" />Dividimos ; cos(x) / cos(x) = 1Sustituimos ; = - 1 / cos(x)sin(x)m = - 1 / cos(x)sin(x)Restamos m a ambos lados ; ( - 1 / cos(x)sin(x)) - m = 0Simplificamos ; = ( - 1 / cos(x)sin(x)) - (mcos(x)sin(x) / cos(x)sin(x))combinar fracciones ; = ( - 1 - mcos(x)sin(x)) / cos(x)sin(x)Aplicamos f(x) / g(x) = 0 ⇒g(x) = 0 - 1 - mcos(x)sin(x) = 0Usamos la identidad : cos(x)sin(x) = sin(2x) / 2 - 1 - msin(2x) / 2 = 0 - msin(2x) / 2 = 1Multiplicamos por 2 y dividimos entre - m a ambos lados ; (2 / - m) - msin(2x) / 2 = 1(2 / - m)sin(2x) = - 2 / m ; m≠0Solución general ; sin(x) = a ⇒ x = sin ^ - 1(a) + 2πn ; x = π + sin ^ - 1(a) + 2πn 2x = sin ^ - 1( - 2 / m) + 2πn, 2x = π + sin ^ - 1( - 2 / m) + 2πnx = (sin ^ - 1( - 2 / m) + 2πn) / 2, x = (π + sin ^ - 1( - 2 / m) + 2πn) / 2.