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Prove sin(z1-z2)=sinz1cosz2-cosz1sinz2 by using Euler's formula.

Prove sin(z1-z2)=sinz1cosz2-cosz1sinz2 by using Euler's formula.
 

Grade:12th pass

1 Answers

Rajat
213 Points
4 years ago
(sinAcosB-sinBcosA) = 1/4[(e^iA-e^-iA)(e^iB+e^-iB)-(e^iB-e^-iB)(e^iA+e^-iA)]
=1/4[2e^i(A-B) - 2e^i(B-A)]
=1/2[ 2sin(A-B)]
= sin(A-B)

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