Prove $forall x in mathbbR$: $[sinh(x)+cosh(x)]^n = cosh(nx)+sinh(nx)$ ; $ nin mathbbQ$ [closed]

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Prove $forall x in mathbbR$: $[sinh(x)+cosh(x)]^n = cosh(nx)+sinh(nx)$ ; $ nin mathbbQ$




algebra-precalculus hyperbolic-functions




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closed as off-topic by Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner Aug 6 at 12:14


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Is it important that $nin mathbbQ$ ?
    – Nosrati
    Aug 6 at 7:16










  • Yes, it important?
    – leotv
    Aug 6 at 7:27










  • It holds for real numbers. but is it hold for $ninmathbbC$ ?
    – Nosrati
    Aug 6 at 7:34















up vote
-2
down vote

favorite
1












How to prove?



Prove $forall x in mathbbR$: $[sinh(x)+cosh(x)]^n = cosh(nx)+sinh(nx)$ ; $ nin mathbbQ$




algebra-precalculus hyperbolic-functions




share|cite|improve this question













closed as off-topic by Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner Aug 6 at 12:14


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Is it important that $nin mathbbQ$ ?
    – Nosrati
    Aug 6 at 7:16










  • Yes, it important?
    – leotv
    Aug 6 at 7:27










  • It holds for real numbers. but is it hold for $ninmathbbC$ ?
    – Nosrati
    Aug 6 at 7:34













up vote
-2
down vote

favorite
1









up vote
-2
down vote

favorite
1






1





How to prove?



Prove $forall x in mathbbR$: $[sinh(x)+cosh(x)]^n = cosh(nx)+sinh(nx)$ ; $ nin mathbbQ$




algebra-precalculus hyperbolic-functions




share|cite|improve this question













How to prove?



Prove $forall x in mathbbR$: $[sinh(x)+cosh(x)]^n = cosh(nx)+sinh(nx)$ ; $ nin mathbbQ$





algebra-precalculus hyperbolic-functions





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 7:23









Jyrki Lahtonen

105k12161355




105k12161355









asked Aug 6 at 4:09









leotv

11




11




closed as off-topic by Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner Aug 6 at 12:14


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner Aug 6 at 12:14


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jyrki Lahtonen, Nosrati, Taroccoesbrocco, amWhy, Jendrik Stelzner
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Is it important that $nin mathbbQ$ ?
    – Nosrati
    Aug 6 at 7:16










  • Yes, it important?
    – leotv
    Aug 6 at 7:27










  • It holds for real numbers. but is it hold for $ninmathbbC$ ?
    – Nosrati
    Aug 6 at 7:34

















  • Is it important that $nin mathbbQ$ ?
    – Nosrati
    Aug 6 at 7:16










  • Yes, it important?
    – leotv
    Aug 6 at 7:27










  • It holds for real numbers. but is it hold for $ninmathbbC$ ?
    – Nosrati
    Aug 6 at 7:34
















Is it important that $nin mathbbQ$ ?
– Nosrati
Aug 6 at 7:16




Is it important that $nin mathbbQ$ ?
– Nosrati
Aug 6 at 7:16












Yes, it important?
– leotv
Aug 6 at 7:27




Yes, it important?
– leotv
Aug 6 at 7:27












It holds for real numbers. but is it hold for $ninmathbbC$ ?
– Nosrati
Aug 6 at 7:34





It holds for real numbers. but is it hold for $ninmathbbC$ ?
– Nosrati
Aug 6 at 7:34











1 Answer
1






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up vote
7
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Solution: note that
$$
sinh(x) + cosh(x) = frac mathrm e^x - mathrm e^-x 2 + frac mathrm e^x + mathrm e^-x 2 = e^x,
$$
and rest is obvious.






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    7
    down vote













    Solution: note that
    $$
    sinh(x) + cosh(x) = frac mathrm e^x - mathrm e^-x 2 + frac mathrm e^x + mathrm e^-x 2 = e^x,
    $$
    and rest is obvious.






    share|cite|improve this answer

























      up vote
      7
      down vote













      Solution: note that
      $$
      sinh(x) + cosh(x) = frac mathrm e^x - mathrm e^-x 2 + frac mathrm e^x + mathrm e^-x 2 = e^x,
      $$
      and rest is obvious.






      share|cite|improve this answer























        up vote
        7
        down vote










        up vote
        7
        down vote









        Solution: note that
        $$
        sinh(x) + cosh(x) = frac mathrm e^x - mathrm e^-x 2 + frac mathrm e^x + mathrm e^-x 2 = e^x,
        $$
        and rest is obvious.






        share|cite|improve this answer













        Solution: note that
        $$
        sinh(x) + cosh(x) = frac mathrm e^x - mathrm e^-x 2 + frac mathrm e^x + mathrm e^-x 2 = e^x,
        $$
        and rest is obvious.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 6 at 4:20









        xbh

        1,6079




        1,6079












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