Demonstrate that equating the real parts of both sides of the equation ej(α+β) = ejαejβ will lead to identity #5 in Table 1. Also, show that identity #4 is obtained from equating the imaginary parts.
Table 1
Some basic trigonometric identities.
Number | Equation |
1 | sin2 θ + cos2 θ = 1 |
2 | cos 2θ = cos2 θ −sin2 θ |
3 | sin 2θ = 2 sin θ cos θ |
4 | sin(α ± β) = sin α cos β ± cos α sin β |
5 | cos(α ± β) = cos α cos β ∓ sin α sin β |
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