El profesor se sorprenderá mucho al ver tu solución correcta😉
2 sec (y) --------- = 2 2 cos (2*x)
a*w^2 + b*w + c = 0
D = b^2 - 4 * a * c =
(0)^2 - 4 * (cos(2*x)^(-2)) * (-2) = 8/cos(2*x)^2
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
/| _________________|\ / _________________\ || ___ ___ / 2 || | / 2 | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 - \/ 1 - 2*cos (2*x) | y1 = - I*log||---------- - --------------------------|| + arg|------------------------| \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) /
/| _________________|\ / _________________\ || ___ ___ / 2 || | / 2 | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-1 + \/ 1 - 2*cos (2*x) | y2 = - I*log||- ---------- + --------------------------|| + arg|-------------------------| \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) /
/| _________________|\ / / _________________\ \ || ___ ___ / 2 || | | / 2 | | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-\1 + \/ 1 - 2*cos (2*x) / | y3 = - I*log||- ---------- - --------------------------|| + arg|----------------------------| \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) /
/| _________________|\ / _________________\ || ___ ___ / 2 || | / 2 | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 + \/ 1 - 2*cos (2*x) | y4 = - I*log||---------- + --------------------------|| + arg|------------------------| \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) /
y4 = -i*log(Abs(sqrt(2)*sqrt(1 - 2*cos(2*x)^2)/(2*cos(2*x)) + sqrt(2)/(2*cos(2*x)))) + arg((sqrt(1 - 2*cos(2*x)^2) + 1)/cos(2*x))
suma
/| _________________|\ / _________________\ /| _________________|\ / _________________\ /| _________________|\ / / _________________\ \ /| _________________|\ / _________________\ || ___ ___ / 2 || | / 2 | || ___ ___ / 2 || | / 2 | || ___ ___ / 2 || | | / 2 | | || ___ ___ / 2 || | / 2 | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 - \/ 1 - 2*cos (2*x) | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-1 + \/ 1 - 2*cos (2*x) | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-\1 + \/ 1 - 2*cos (2*x) / | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 + \/ 1 - 2*cos (2*x) | - I*log||---------- - --------------------------|| + arg|------------------------| + - I*log||- ---------- + --------------------------|| + arg|-------------------------| + - I*log||- ---------- - --------------------------|| + arg|----------------------------| + - I*log||---------- + --------------------------|| + arg|------------------------| \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) / \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) / \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) / \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) /
=
/| _________________|\ /| _________________|\ /| _________________|\ /| _________________|\ / _________________\ / _________________\ / _________________\ / / _________________\ \ || ___ ___ / 2 || || ___ ___ / 2 || || ___ ___ / 2 || || ___ ___ / 2 || | / 2 | | / 2 | | / 2 | | | / 2 | | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 + \/ 1 - 2*cos (2*x) | |1 - \/ 1 - 2*cos (2*x) | |-1 + \/ 1 - 2*cos (2*x) | |-\1 + \/ 1 - 2*cos (2*x) / | - I*log||---------- + --------------------------|| - I*log||---------- - --------------------------|| - I*log||- ---------- + --------------------------|| - I*log||- ---------- - --------------------------|| + arg|------------------------| + arg|------------------------| + arg|-------------------------| + arg|----------------------------| \|2*cos(2*x) 2*cos(2*x) |/ \|2*cos(2*x) 2*cos(2*x) |/ \| 2*cos(2*x) 2*cos(2*x) |/ \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) / \ cos(2*x) / \ cos(2*x) / \ cos(2*x) /
producto
/ /| _________________|\ / _________________\\ / /| _________________|\ / _________________\\ / /| _________________|\ / / _________________\ \\ / /| _________________|\ / _________________\\ | || ___ ___ / 2 || | / 2 || | || ___ ___ / 2 || | / 2 || | || ___ ___ / 2 || | | / 2 | || | || ___ ___ / 2 || | / 2 || | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 - \/ 1 - 2*cos (2*x) || | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-1 + \/ 1 - 2*cos (2*x) || | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |-\1 + \/ 1 - 2*cos (2*x) / || | || \/ 2 \/ 2 *\/ 1 - 2*cos (2*x) || |1 + \/ 1 - 2*cos (2*x) || |- I*log||---------- - --------------------------|| + arg|------------------------||*|- I*log||- ---------- + --------------------------|| + arg|-------------------------||*|- I*log||- ---------- - --------------------------|| + arg|----------------------------||*|- I*log||---------- + --------------------------|| + arg|------------------------|| \ \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) // \ \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) // \ \| 2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) // \ \|2*cos(2*x) 2*cos(2*x) |/ \ cos(2*x) //
=
/ / _________________\ / /| _________________|\\\ / / _________________\ / /| _________________|\\\ / / _________________\ / /| _________________|\\\ / / / _________________\ \ / /| _________________|\\\ | | / 2 | | || / 2 |||| | | / 2 | | || / 2 |||| | | / 2 | | || / 2 |||| | | | / 2 | | | || / 2 |||| | |1 + \/ 1 - 2*cos (2*x) | | log(2) ||1 + \/ 1 - 2*cos (2*x) |||| | |1 - \/ 1 - 2*cos (2*x) | | log(2) ||-1 + \/ 1 - 2*cos (2*x) |||| | |-1 + \/ 1 - 2*cos (2*x) | | log(2) ||-1 + \/ 1 - 2*cos (2*x) |||| | |-\1 + \/ 1 - 2*cos (2*x) / | | log(2) ||1 + \/ 1 - 2*cos (2*x) |||| |- arg|------------------------| + I*|- ------ + log||------------------------||||*|- arg|------------------------| + I*|- ------ + log||-------------------------||||*|- arg|-------------------------| + I*|- ------ + log||-------------------------||||*|- arg|----------------------------| + I*|- ------ + log||------------------------|||| \ \ cos(2*x) / \ 2 \| cos(2*x) |/// \ \ cos(2*x) / \ 2 \| cos(2*x) |/// \ \ cos(2*x) / \ 2 \| cos(2*x) |/// \ \ cos(2*x) / \ 2 \| cos(2*x) |///
(-arg((1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)) + i*(-log(2)/2 + log(Abs((1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)))))*(-arg((1 - sqrt(1 - 2*cos(2*x)^2))/cos(2*x)) + i*(-log(2)/2 + log(Abs((-1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)))))*(-arg((-1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)) + i*(-log(2)/2 + log(Abs((-1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)))))*(-arg(-(1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)) + i*(-log(2)/2 + log(Abs((1 + sqrt(1 - 2*cos(2*x)^2))/cos(2*x)))))