Respuestas
Respuesta dada por:
2
1.-
Recordemos:
• sec x = 1 / cos x
• 1 - cos²x = sen²x
PROCEDIMIENTO:
![{\sec x -\cos x =}\\\\{\dfrac{1}{\cos x}- \cos x=}\\\\\\{\dfrac{1-\cos ^2x}{\cos x}=}\\\\\\{\dfrac{\sin ^2 x}{\cos }=}\\\\\\{\dfrac{\sin x}{1 }.\dfrac{\sin x}{\cos x}=}\\\\\\{\boxed{\sin x.\tan x}\ \ \ \ l.q.q.d.} {\sec x -\cos x =}\\\\{\dfrac{1}{\cos x}- \cos x=}\\\\\\{\dfrac{1-\cos ^2x}{\cos x}=}\\\\\\{\dfrac{\sin ^2 x}{\cos }=}\\\\\\{\dfrac{\sin x}{1 }.\dfrac{\sin x}{\cos x}=}\\\\\\{\boxed{\sin x.\tan x}\ \ \ \ l.q.q.d.}](https://tex.z-dn.net/?f=%7B%5Csec+x+-%5Ccos+x+%3D%7D%5C%5C%5C%5C%7B%5Cdfrac%7B1%7D%7B%5Ccos+x%7D-+%5Ccos+x%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cdfrac%7B1-%5Ccos+%5E2x%7D%7B%5Ccos+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cdfrac%7B%5Csin+%5E2+x%7D%7B%5Ccos+%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cdfrac%7B%5Csin+x%7D%7B1+%7D.%5Cdfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cboxed%7B%5Csin+x.%5Ctan+x%7D%5C+%5C+%5C+%5C+l.q.q.d.%7D)
2.-
Recordemos:
• cot x = cos x / sen x
• sen²x + cos²x = 1
Procedimiento:
![{\sin x + \cos x.\cot x=}\\\\\\{\sin x + \dfrac{\cos x}{1}.\dfrac{\cos x}{\sin x}=}\\\\\\{\sin x + \dfrac{\cos^2x}{\sin x}=}\\\\\\{\dfrac{\sin^2x+\cos^2x}{\sin x}=}\\\\\\{\dfrac{1}{\sin x}=}\\\\\\{\boxed{\csc x}\ \ \ \ l.q.q.d} {\sin x + \cos x.\cot x=}\\\\\\{\sin x + \dfrac{\cos x}{1}.\dfrac{\cos x}{\sin x}=}\\\\\\{\sin x + \dfrac{\cos^2x}{\sin x}=}\\\\\\{\dfrac{\sin^2x+\cos^2x}{\sin x}=}\\\\\\{\dfrac{1}{\sin x}=}\\\\\\{\boxed{\csc x}\ \ \ \ l.q.q.d}](https://tex.z-dn.net/?f=%7B%5Csin+x+%2B+%5Ccos+x.%5Ccot+x%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Csin+x+%2B+%5Cdfrac%7B%5Ccos+x%7D%7B1%7D.%5Cdfrac%7B%5Ccos+x%7D%7B%5Csin+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Csin+x+%2B+%5Cdfrac%7B%5Ccos%5E2x%7D%7B%5Csin+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cdfrac%7B%5Csin%5E2x%2B%5Ccos%5E2x%7D%7B%5Csin+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cdfrac%7B1%7D%7B%5Csin+x%7D%3D%7D%5C%5C%5C%5C%5C%5C%7B%5Cboxed%7B%5Ccsc+x%7D%5C+%5C+%5C+%5C+l.q.q.d%7D)
Salu2.!! :)
Wellington
Recordemos:
• sec x = 1 / cos x
• 1 - cos²x = sen²x
PROCEDIMIENTO:
2.-
Recordemos:
• cot x = cos x / sen x
• sen²x + cos²x = 1
Procedimiento:
Salu2.!! :)
Wellington
kaybo2014p074ao:
Muchas gracias :D !
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