I have been trying to simplify this expression: cos ⁡ ( θ ) − 1...

Dania Mueller

Dania Mueller

Answered

2022-07-01

I have been trying to simplify this expression:
cos ( θ ) 1 cos ( θ ) + i sin ( θ )

Answer & Explanation

Kaydence Washington

Kaydence Washington

Expert

2022-07-02Added 32 answers

c o s ( θ ) 1 cos ( θ ) + i sin ( θ ) = c o s ( θ ) 1 e i θ =
c o s ( θ ) e i θ = 1 2 e i θ + 1 2 e i θ e i θ =
= 1 2 e i θ 1 2 e i θ = i ( 1 2 i e i θ 1 2 i e i θ ) = i sin ( θ )
Gaaljh

Gaaljh

Expert

2022-07-03Added 7 answers

HINT:
e i θ = cos ( θ ) + i sin ( θ ) = cos θ i sin θ
cos θ i sin θ = 1 cos θ + i sin θ
which is also evident from ( cos θ + i sin θ ) ( cos θ i sin θ ) = = 1

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