El profesor se sorprenderá mucho al ver tu solución correcta😉
(a - 2)*sin(x) + cos(x) = a
/ / _________ \\ / / _________ \\ | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a|| x1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| \ \ 1 + a // \ \ 1 + a //
/ / _________\\ / / _________\\ | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a || x2 = 2*re|atan|--------------------|| + 2*I*im|atan|--------------------|| \ \ 1 + a // \ \ 1 + a //
x2 = 2*re(atan((a + sqrt(5 - 4*a) - 2)/(a + 1))) + 2*i*im(atan((a + sqrt(5 - 4*a) - 2)/(a + 1)))
suma
/ / _________ \\ / / _________ \\ / / _________\\ / / _________\\ | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a || - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|--------------------|| + 2*I*im|atan|--------------------|| \ \ 1 + a // \ \ 1 + a // \ \ 1 + a // \ \ 1 + a //
=
/ / _________ \\ / / _________\\ / / _________ \\ / / _________\\ | |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a || | |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a || - 2*re|atan|-------------------|| + 2*re|atan|--------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|--------------------|| \ \ 1 + a // \ \ 1 + a // \ \ 1 + a // \ \ 1 + a //
producto
/ / / _________ \\ / / _________ \\\ / / / _________\\ / / _________\\\ | | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a||| | | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||| |- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|--------------------|| + 2*I*im|atan|--------------------||| \ \ \ 1 + a // \ \ 1 + a /// \ \ \ 1 + a // \ \ 1 + a ///
=
/ / / _________\\ / / _________\\\ / / / _________ \\ / / _________ \\\ | | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||| | | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a||| -4*|I*im|atan|--------------------|| + re|atan|--------------------|||*|I*im|atan|-------------------|| + re|atan|-------------------||| \ \ \ 1 + a // \ \ 1 + a /// \ \ \ 1 + a // \ \ 1 + a ///
-4*(i*im(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))) + re(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))))*(i*im(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))) + re(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))))