Respuestas
Respuesta dada por:
1
Realizar transformaciones con identidades trigonométricas:
![\[\left( {\sec \left( \beta \right) + \tan \left( \beta \right)} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cleft%28+%7B%5Csec+%5Cleft%28+%5Cbeta++%5Cright%29+%2B+%5Ctan+%5Cleft%28+%5Cbeta++%5Cright%29%7D+%5Cright%29%5Cleft%28+%7B1+-+%5Csin+%5Cleft%28+%5Cbeta++%5Cright%29%7D+%5Cright%29+%3D+1%5C%5D+%5C%5C+ "\[\left( {\sec \left( \beta \right) + \tan \left( \beta \right)} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\")
![\[\left( {\frac{1}{{\cos \left( \beta \right)}} + \frac{{\sin \left( \beta \right)}}{{\cos \left( \beta \right)}}} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cleft%28+%7B%5Cfrac%7B1%7D%7B%7B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D+%2B+%5Cfrac%7B%7B%5Csin+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D%7B%7B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D%7D+%5Cright%29%5Cleft%28+%7B1+-+%5Csin+%5Cleft%28+%5Cbeta++%5Cright%29%7D+%5Cright%29+%3D+1%5C%5D+%5C%5C+ "\[\left( {\frac{1}{{\cos \left( \beta \right)}} + \frac{{\sin \left( \beta \right)}}{{\cos \left( \beta \right)}}} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\")
![\[\frac{1}{{\cos \left( \beta \right)}}\left( {1 + \sin \left( \beta \right)} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B%7B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D%5Cleft%28+%7B1+%2B+%5Csin+%5Cleft%28+%5Cbeta++%5Cright%29%7D+%5Cright%29%5Cleft%28+%7B1+-+%5Csin+%5Cleft%28+%5Cbeta++%5Cright%29%7D+%5Cright%29+%3D+1%5C%5D+%5C%5C+ "\[\frac{1}{{\cos \left( \beta \right)}}\left( {1 + \sin \left( \beta \right)} \right)\left( {1 - \sin \left( \beta \right)} \right) = 1\] \\")
![\[\frac{1}{{\cos \left( \beta \right)}}\left( {1 - \sin {{\left( \beta \right)}^2}} \right) = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B%7B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D%5Cleft%28+%7B1+-+%5Csin+%7B%7B%5Cleft%28+%5Cbeta++%5Cright%29%7D%5E2%7D%7D+%5Cright%29+%3D+1%5C%5D+%5C%5C+ "\[\frac{1}{{\cos \left( \beta \right)}}\left( {1 - \sin {{\left( \beta \right)}^2}} \right) = 1\] \\")
![\[\frac{{\cos {{\left( \beta \right)}^2}}}{{\cos \left( \beta \right)}} = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B%7B%5Ccos+%7B%7B%5Cleft%28+%5Cbeta++%5Cright%29%7D%5E2%7D%7D%7D%7B%7B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29%7D%7D+%3D+1%5C%5D+%5C%5C+ "\[\frac{{\cos {{\left( \beta \right)}^2}}}{{\cos \left( \beta \right)}} = 1\] \\")
![\[\cos \left( \beta \right) = 1\] \\](https://tex.z-dn.net/?f=%5C%5B%5Ccos+%5Cleft%28+%5Cbeta++%5Cright%29+%3D+1%5C%5D+%5C%5C+ "\[\cos \left( \beta \right) = 1\] \\")
El angulo que satisface es:
![\[\beta = arc\cos \left( 1 \right)\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cbeta++%3D+arc%5Ccos+%5Cleft%28+1+%5Cright%29%5C%5D+%5C%5C+ "\[\beta = arc\cos \left( 1 \right)\] \\")
Finalmente:
![\[\beta = 0\] \\](https://tex.z-dn.net/?f=%5C%5B%5Cbeta++%3D+0%5C%5D+%5C%5C+ "\[\beta = 0\] \\")
El angulo que satisface es:
Finalmente:
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