Respuestas
Respuesta dada por:
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Calcule el valor de la siguiente expresión:
(sen 45° + cos 60°)(csc 45° - tan 45°)
![(sen 45\° + cos 60\°)(csc 45\° - tan 45\°)= \\ \\ \\ csc 45\º= \dfrac{1}{sen\ 45\º}\qquad\qquad tan45\º = \dfrac{sen\ 45\º}{cos\ 45\º} \qquad sen\ 45\º = cos\ 45\º\\ \\ \\ (sen 45\° + cos 60\°)(\dfrac{1}{sen\ 45\º} - \dfrac{sen\ 45\º}{cos\ 45\º})=\\ \\ \\ ( \frac{ \sqrt{2}}{2} + \frac{1}{2})(\dfrac{1}{\frac{ \sqrt{2}}{2}} - \dfrac{\frac{ \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}})= (sen 45\° + cos 60\°)(csc 45\° - tan 45\°)= \\ \\ \\ csc 45\º= \dfrac{1}{sen\ 45\º}\qquad\qquad tan45\º = \dfrac{sen\ 45\º}{cos\ 45\º} \qquad sen\ 45\º = cos\ 45\º\\ \\ \\ (sen 45\° + cos 60\°)(\dfrac{1}{sen\ 45\º} - \dfrac{sen\ 45\º}{cos\ 45\º})=\\ \\ \\ ( \frac{ \sqrt{2}}{2} + \frac{1}{2})(\dfrac{1}{\frac{ \sqrt{2}}{2}} - \dfrac{\frac{ \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}})=](https://tex.z-dn.net/?f=%28sen+45%5C%C2%B0+%2B+cos+60%5C%C2%B0%29%28csc+45%5C%C2%B0+-+tan+45%5C%C2%B0%29%3D++%5C%5C++%5C%5C++%5C%5C+csc+45%5C%C2%BA%3D++%5Cdfrac%7B1%7D%7Bsen%5C+45%5C%C2%BA%7D%5Cqquad%5Cqquad+tan45%5C%C2%BA+%3D++%5Cdfrac%7Bsen%5C+45%5C%C2%BA%7D%7Bcos%5C+45%5C%C2%BA%7D+%5Cqquad+sen%5C+45%5C%C2%BA+%3D+cos%5C+45%5C%C2%BA%5C%5C++%5C%5C++%5C%5C+%28sen+45%5C%C2%B0+%2B+cos+60%5C%C2%B0%29%28%5Cdfrac%7B1%7D%7Bsen%5C+45%5C%C2%BA%7D+-++%5Cdfrac%7Bsen%5C+45%5C%C2%BA%7D%7Bcos%5C+45%5C%C2%BA%7D%29%3D%5C%5C++%5C%5C++%5C%5C+%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D+%2B+%5Cfrac%7B1%7D%7B2%7D%29%28%5Cdfrac%7B1%7D%7B%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%7D+-++%5Cdfrac%7B%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%7D%7B%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%7D%29%3D)
![( \frac{ \sqrt{2}}{2} + \frac{1}{2})( \dfrac{\frac{2- \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}})= \\ \\ \\ ( \dfrac{ \sqrt{2}+1}{2} )( \dfrac{2- \sqrt{2}}{ \sqrt{2}})= \\ \\ Racionalizamos \to \dfrac{2- \sqrt{2}}{ \sqrt{2}}* \dfrac{\sqrt{2}}{ \sqrt{2}}= \dfrac{2\sqrt{2}-2}{ 2} \\ \\ \\ \left( \dfrac{ \sqrt{2}+1}{2} \right)\left( \dfrac{2\sqrt{2}-2}{ 2}\right )= \dfrac{2 \sqrt{2}^2 -2 \sqrt{2} +2 \sqrt{2}-2}{4}= ( \frac{ \sqrt{2}}{2} + \frac{1}{2})( \dfrac{\frac{2- \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}})= \\ \\ \\ ( \dfrac{ \sqrt{2}+1}{2} )( \dfrac{2- \sqrt{2}}{ \sqrt{2}})= \\ \\ Racionalizamos \to \dfrac{2- \sqrt{2}}{ \sqrt{2}}* \dfrac{\sqrt{2}}{ \sqrt{2}}= \dfrac{2\sqrt{2}-2}{ 2} \\ \\ \\ \left( \dfrac{ \sqrt{2}+1}{2} \right)\left( \dfrac{2\sqrt{2}-2}{ 2}\right )= \dfrac{2 \sqrt{2}^2 -2 \sqrt{2} +2 \sqrt{2}-2}{4}=](https://tex.z-dn.net/?f=+%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D+%2B+%5Cfrac%7B1%7D%7B2%7D%29%28++%5Cdfrac%7B%5Cfrac%7B2-+%5Csqrt%7B2%7D%7D%7B2%7D%7D%7B%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%7D%29%3D++%5C%5C++%5C%5C++%5C%5C++%28+%5Cdfrac%7B+%5Csqrt%7B2%7D%2B1%7D%7B2%7D+%29%28++%5Cdfrac%7B2-+%5Csqrt%7B2%7D%7D%7B+%5Csqrt%7B2%7D%7D%29%3D++%5C%5C++%5C%5C++Racionalizamos+%5Cto++%5Cdfrac%7B2-+%5Csqrt%7B2%7D%7D%7B+%5Csqrt%7B2%7D%7D%2A+%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B+%5Csqrt%7B2%7D%7D%3D++%5Cdfrac%7B2%5Csqrt%7B2%7D-2%7D%7B+2%7D++%5C%5C++%5C%5C++%5C%5C++%5Cleft%28+%5Cdfrac%7B+%5Csqrt%7B2%7D%2B1%7D%7B2%7D+%5Cright%29%5Cleft%28++%5Cdfrac%7B2%5Csqrt%7B2%7D-2%7D%7B+2%7D%5Cright+%29%3D++%5Cdfrac%7B2+%5Csqrt%7B2%7D%5E2+-2+%5Csqrt%7B2%7D+%2B2+%5Csqrt%7B2%7D-2%7D%7B4%7D%3D+++)
![\dfrac{2*2 -2 \sqrt{2} +2 \sqrt{2}-2}{4}= \qquad se \ cancelan \ 2 \sqrt{2} \\ \\ \\ \dfrac{2*2 - 2}{4}= \dfrac{4-2}{4} = \dfrac{2}{4} = \boxed{ \dfrac{1}{2}} \\ \\ \\ \boxed{(sen 45\° + cos 60\°)(csc 45\° - tan 45\°)= \boxed{ \dfrac{1}{2}}} \dfrac{2*2 -2 \sqrt{2} +2 \sqrt{2}-2}{4}= \qquad se \ cancelan \ 2 \sqrt{2} \\ \\ \\ \dfrac{2*2 - 2}{4}= \dfrac{4-2}{4} = \dfrac{2}{4} = \boxed{ \dfrac{1}{2}} \\ \\ \\ \boxed{(sen 45\° + cos 60\°)(csc 45\° - tan 45\°)= \boxed{ \dfrac{1}{2}}}](https://tex.z-dn.net/?f=+%5Cdfrac%7B2%2A2+-2+%5Csqrt%7B2%7D+%2B2+%5Csqrt%7B2%7D-2%7D%7B4%7D%3D+%5Cqquad+se+%5C+cancelan+%5C+2+%5Csqrt%7B2%7D++++%5C%5C++%5C%5C++%5C%5C++%5Cdfrac%7B2%2A2+-+2%7D%7B4%7D%3D++%5Cdfrac%7B4-2%7D%7B4%7D+%3D++++%5Cdfrac%7B2%7D%7B4%7D+%3D++%5Cboxed%7B++%5Cdfrac%7B1%7D%7B2%7D%7D+%5C%5C++%5C%5C++%5C%5C++%5Cboxed%7B%28sen+45%5C%C2%B0+%2B+cos+60%5C%C2%B0%29%28csc+45%5C%C2%B0+-+tan+45%5C%C2%B0%29%3D+%5Cboxed%7B++%5Cdfrac%7B1%7D%7B2%7D%7D%7D+)
Espero que te sirva, salu2!!!!
(sen 45° + cos 60°)(csc 45° - tan 45°)
Espero que te sirva, salu2!!!!
jose988:
racias
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