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Express 10e^x - 22e^-x in terms of sinh and cosh?
Step by Step will be given best answer
2 Answers
- Someone AngryLv 58 years agoFavorite Answer
You want to find a and b such that
a sinh(x) + b cosh(x) = 10e^x - 22e^(-x)
Since sinh(x) = (1/2) (e^x - e^-x) and cosh(x) = (1/2) (e^x + e^-x),
a/2 (e^x - e^-x) + b/2 (e^x + e^-x) = 10e^x - 22e^-x
(a + b)/2 e^x + (-a +b)/2 e^-x = 10e^x - 22e^-x
Just match up the coefficients; we have
a + b = 20
-a + b = -44
So b = -12 and a = 32. Hence the answer is 32 sinh(x) - 12 cosh(x).
- BrambleLv 78 years ago
By adding / subtracting 6.e^(x) and 6.e(-x) respectively the given expression may immediately be re-written
= [16â®^x - 16â®^(-x)] – [6.â®^(x) + 6.â®^(-x)]
= 32.sinh(x) – 12.cosh(x)
