What is csc(theta/2) in terms of trigonometric functions of a unit theta?

Cullen Banks

Cullen Banks

Answered question

2023-03-14

What is csc ( θ 2 ) in terms of trigonometric functions of a unit θ ?

Answer & Explanation

Edwin Simmons

Edwin Simmons

Beginner2023-03-15Added 6 answers

Recall cos 2 A = 1 - 2 sin 2 A
i.e. 2 sin 2 A = 1 - cos 2 A
or sin 2 A = 1 - cos 2 A 2
or sin A = 1 - cos 2 A 2
Putting 2 A = θ or A = θ 2
Therefore, sin ( θ 2 ) = 1 - cos θ 2
or csc ( θ 2 ) = 2 1 - cos θ

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