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