I am trying to follow a solution to a problem and it says that (

Brock Byrd

Brock Byrd

Answered question

2022-06-29

I am trying to follow a solution to a problem and it says that ( 1 + i tan θ 1 i tan θ ) a = ( cos θ + i sin θ cos θ i sin θ ) a
However, I am unable to see why this would be? It is probably just a simple oversight but I am unsure.

Answer & Explanation

Dayana Zuniga

Dayana Zuniga

Beginner2022-06-30Added 16 answers

Simply multiply both the numerator and denominator of the left hand side (within the parentheses) by cos θ and note that tan θ = sin θ / cos θ
( cos θ ( 1 + i sin θ cos θ ) cos θ ( 1 i sin θ cos θ ) ) a
Joel French

Joel French

Beginner2022-07-01Added 10 answers

( 1 + i tan θ 1 i tan θ ) a = ( cos θ + i cos θ tan θ cos θ i cos θ tan θ ) a = ( cos θ + i sin θ cos θ i sin θ ) a
Since
tan θ = sin θ cos θ

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