¡ SOLO PARA LOS VERDADEROS TIGRES?

Trataremos de abreviar procedimiento

1) Sea

<img src="https://tex.z-dn.net/?f=a%3D%5Csin%20f%5Ccos%20x%5C%5C%0Ab%3D%5Ccos%20f%5Ccos%20x%5C%5C%0Ac%3D%5Csin%20x" />

entonces en el numerador tenemos algo como

<img src="https://tex.z-dn.net/?f=N%3D%28a%20%2B%20b%20%2B%20c%29%5E5%20%2B%20%28a%20-%20b%20-%20c%29%5E5%20-%20%28a%20%2B%20b%20-%20c%29%5E5%20-%20%28a%20-%20b%20%2B%20c%29%5E5" />

2) Pongamos

y = b + c

z = b - c

entonces

<img src="https://tex.z-dn.net/?f=N%3D%28a%20%2B%20y%29%5E5%20%2B%20%28a%20-%20y%29%5E5%20-%20%28a%20%2B%20z%29%5E5%20-%20%28a%20-%20z%29%5E5%5C%5C%20%5C%5C%0AN%3D2%28a%5E5%2B10a%5E3y%5E2%2B5ay%5E4%29-2%28a%5E5%2B10a%5E3z%5E2%2B5az%5E4%29%5C%5C%20%5C%5C%0AN%3D2a%28a%5E4%2B10a%5E2y%5E2%2B5y%5E4%29-2a%28a%5E4%2B10a%5E2z%5E2%2B5z%5E4%29%5C%5C%20%5C%5C%0AN%3D2a%2810a%5E2y%5E2%2B5y%5E4-10a%5E2z%5E2-5z%5E4%29%5C%5C%20%5C%5C%0AN%3D10a%5B%28y%5E4-z%5E4%29%2B2a%5E2%28y%5E2-z%5E2%29%5D%5C%5C%20%5C%5C%0AN%3D10a%28y%5E2-z%5E2%29%28y%5E2%2Bz%5E2%2B2a%5E2%29%5C%5C%20%5C%5C%0AN%3D10a%28y-z%29%28y%2Bz%29%282b%5E2%2B2c%5E2%2B2a%5E2%29%5C%5C%20%5C%5C%0AN%3D10a%282c%29%282b%29%282b%5E2%2B2c%5E2%2B2a%5E2%29%5C%5C%20%5C%5C%0A%5Cboxed%7BN%3D80abc%28a%5E2%2Bb%5E2%2Bc%5E2%29%7D" />

3) En el denominador tenemos <img src="https://tex.z-dn.net/?f=D%3D%2016abc" /> por ende

<img src="https://tex.z-dn.net/?f=R%3D%5Cdfrac%7B80abc%28a%5E2%2Bb%5E2%2Bc%5E2%29%7D%7B16abc%7D%3D5%28a%5E2%2Bb%5E2%2Bc%5E2%29%5C%5C%20%5C%5C%20%5C%5C%0AR%3D5%5B%28%5Csin%20f%5Ccos%20x%29%5E2%2B%28%5Ccos%20f%5Ccos%20x%29%5E2%2B%28%5Csin%20x%29%5E2%5D%5C%5C%20%5C%5C%20%0AR%3D5%5B%5Ccos%5E2x%2B%5Csin%5E2x%5D%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7BR%3D5%7D%7D" />.