Cual de las siguientes expresiones son iguales que sen 40 grados más coseno de 50 grados
1) 2Sen 40
2)2coseno de 50
3) sen 50 +coseno de 40 grados
Respuestas
Respuesta dada por:
39
Debes aplicar un par de propiedades:
![sen(a\pm b)=sen(a)\cdot cos(b)\pm sen(b)\cdot cos(a) \\ cos(a\pm b)=cos(a)\cdot cos(b)\mp sen(a)\cdot sen(b) \\ \\ sen(45)= \frac{ \sqrt{2} }{2}=cos(45) sen(a\pm b)=sen(a)\cdot cos(b)\pm sen(b)\cdot cos(a) \\ cos(a\pm b)=cos(a)\cdot cos(b)\mp sen(a)\cdot sen(b) \\ \\ sen(45)= \frac{ \sqrt{2} }{2}=cos(45)](https://tex.z-dn.net/?f=sen%28a%5Cpm+b%29%3Dsen%28a%29%5Ccdot+cos%28b%29%5Cpm+sen%28b%29%5Ccdot+cos%28a%29+%5C%5C+cos%28a%5Cpm+b%29%3Dcos%28a%29%5Ccdot+cos%28b%29%5Cmp+sen%28a%29%5Ccdot+sen%28b%29+%5C%5C++%5C%5C+sen%2845%29%3D+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D%3Dcos%2845%29+)
En tu problema:
![sen(40)=sen(45-5)= \\ sen(45)\cdot cos(5)-sen(5)\cdot cos(45)=\\sen(45)\cdot cos(5)-sen(5)\cdot sen(45)=\\sen(45)(cos(5)-sen(5)) \\ \\ cos(50)=cos(45+5)=\\cos(45)\cdot cos(5)-sen(45)\cdot sen(5)=\\sen(45)\cdot cos(5)-sen(45)\cdot sen(5)=\\sen(45)(cos(5)-sen(5)) =sen(40)\\ \\ entonces: \\ \boxed{cos(50)=sen(40)} sen(40)=sen(45-5)= \\ sen(45)\cdot cos(5)-sen(5)\cdot cos(45)=\\sen(45)\cdot cos(5)-sen(5)\cdot sen(45)=\\sen(45)(cos(5)-sen(5)) \\ \\ cos(50)=cos(45+5)=\\cos(45)\cdot cos(5)-sen(45)\cdot sen(5)=\\sen(45)\cdot cos(5)-sen(45)\cdot sen(5)=\\sen(45)(cos(5)-sen(5)) =sen(40)\\ \\ entonces: \\ \boxed{cos(50)=sen(40)}](https://tex.z-dn.net/?f=sen%2840%29%3Dsen%2845-5%29%3D+%5C%5C+sen%2845%29%5Ccdot+cos%285%29-sen%285%29%5Ccdot+cos%2845%29%3D%5C%5Csen%2845%29%5Ccdot+cos%285%29-sen%285%29%5Ccdot+sen%2845%29%3D%5C%5Csen%2845%29%28cos%285%29-sen%285%29%29+%5C%5C++%5C%5C+cos%2850%29%3Dcos%2845%2B5%29%3D%5C%5Ccos%2845%29%5Ccdot+cos%285%29-sen%2845%29%5Ccdot+sen%285%29%3D%5C%5Csen%2845%29%5Ccdot+cos%285%29-sen%2845%29%5Ccdot+sen%285%29%3D%5C%5Csen%2845%29%28cos%285%29-sen%285%29%29+%3Dsen%2840%29%5C%5C++%5C%5C+entonces%3A+%5C%5C+%5Cboxed%7Bcos%2850%29%3Dsen%2840%29%7D)
![sen(40)+cos(50)=sen(40)+sen(40)=cos(50)+cos(50)\\=2cos(50)=2sen(40) sen(40)+cos(50)=sen(40)+sen(40)=cos(50)+cos(50)\\=2cos(50)=2sen(40)](https://tex.z-dn.net/?f=sen%2840%29%2Bcos%2850%29%3Dsen%2840%29%2Bsen%2840%29%3Dcos%2850%29%2Bcos%2850%29%5C%5C%3D2cos%2850%29%3D2sen%2840%29)
Opción 1 y 2
Saludos!
En tu problema:
Opción 1 y 2
Saludos!
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