Can This Exponential Identity Be Proven?

Thread starter hariyo
Start date Jan 20, 2011
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Exponential Identity

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SUMMARY

The exponential identity exp(jAt) + exp(jBt) = 2exp(j(A+B)/2)cos((A-B)/2) has been proven through a series of transformations. The proof involves multiplying both sides by exp(-j(A+B)t/2) and simplifying using Euler's formula. The final expression confirms the identity by demonstrating that the left-hand side equals the right-hand side through the use of cosine functions and exponential terms.

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Jan 20, 2011

hariyo

Does anyone know how to prove this?

exp(jAt)+exp(jBt)= 2exp(j(A+B)/2)cos((A-B)/2)

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Jan 20, 2011

hariyo

Sorry I think i know by now. Here is the solution.

exp(jAt)+exp(jBt)= 2exp(j(A+B)/2)cos((A-B)/2)

(exp(jAt)+exp(jBt) ) exp(-j(A+B)t/2) exp(+j(A+B)t/2)

(exp(j(A-B)t/2)+exp(-j(A-B)t/2) ) exp(+j(A+B)t/2)

cos((A-B)t/2) 2exp(j(A+B)/2)t