demostrar lo siguiente
1) sen^4 r - cos ^4 r = sen^2 r - cos^2 r
2) cot x = csc x - 1
csc x +1 cot x
Respuestas
Respuesta dada por:
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sen^4 r - cos ^4 r = sen^2 r - cos^2 r
![sen^{4}r-cos^{4}r=sen^{2}r-cos^{2}r \\ \\ (sen^{2}r+cos^{2}r)(sen^{2}r-cos^{2}r)=sen^{2}r-cos^{2}r \\ \\ 1(sen^{2}r-cos^{2}r)=sen^{2}r-cos^{2}r \\ \\ sen^{2}r-cos^{2}r=sen^{2}r-cos^{2}r sen^{4}r-cos^{4}r=sen^{2}r-cos^{2}r \\ \\ (sen^{2}r+cos^{2}r)(sen^{2}r-cos^{2}r)=sen^{2}r-cos^{2}r \\ \\ 1(sen^{2}r-cos^{2}r)=sen^{2}r-cos^{2}r \\ \\ sen^{2}r-cos^{2}r=sen^{2}r-cos^{2}r](https://tex.z-dn.net/?f=sen%5E%7B4%7Dr-cos%5E%7B4%7Dr%3Dsen%5E%7B2%7Dr-cos%5E%7B2%7Dr+%5C%5C++%5C%5C+%28sen%5E%7B2%7Dr%2Bcos%5E%7B2%7Dr%29%28sen%5E%7B2%7Dr-cos%5E%7B2%7Dr%29%3Dsen%5E%7B2%7Dr-cos%5E%7B2%7Dr+%5C%5C++%5C%5C+1%28sen%5E%7B2%7Dr-cos%5E%7B2%7Dr%29%3Dsen%5E%7B2%7Dr-cos%5E%7B2%7Dr+%5C%5C++%5C%5C+sen%5E%7B2%7Dr-cos%5E%7B2%7Dr%3Dsen%5E%7B2%7Dr-cos%5E%7B2%7Dr)
2) cot x = csc x - 1
csc x +1 cot x
![\frac{cotx}{cscx+1} = \frac{cscx-1}{cotx} \\ \\ cotx(cotx)=(cscx-1)(csc+1) \\ \\ cot^{2}x=csc^{2}x-1 \\ \\ cot^{2}x=cot^{2}x \frac{cotx}{cscx+1} = \frac{cscx-1}{cotx} \\ \\ cotx(cotx)=(cscx-1)(csc+1) \\ \\ cot^{2}x=csc^{2}x-1 \\ \\ cot^{2}x=cot^{2}x](https://tex.z-dn.net/?f=+%5Cfrac%7Bcotx%7D%7Bcscx%2B1%7D+%3D+%5Cfrac%7Bcscx-1%7D%7Bcotx%7D+%5C%5C++%5C%5C+cotx%28cotx%29%3D%28cscx-1%29%28csc%2B1%29+%5C%5C++%5C%5C+cot%5E%7B2%7Dx%3Dcsc%5E%7B2%7Dx-1+%5C%5C++%5C%5C+cot%5E%7B2%7Dx%3Dcot%5E%7B2%7Dx)
2) cot x = csc x - 1
csc x +1 cot x
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