How to use the half angle formula to prove (cos(theta/2)-sin(theta/2))^2?

aphethwevdz

aphethwevdz

Answered question

2023-02-04

How to use the half angle formula to prove ( cos ( θ 2 ) - sin ( θ 2 ) ) 2 ?

Answer & Explanation

Sakroar4

Sakroar4

Beginner2023-02-05Added 4 answers

There is no equation in the question, so it seems as though something has been left out.
However, we are using the formulas sin A = 2 sin ( A 2 ) cos ( A 2 ) and sin 2 A + cos 2 A = 1 and arriving at a likely result.
( cos ( θ 2 ) - sin ( θ 2 ) ) 2
= cos 2 ( θ 2 ) + sin 2 ( θ 2 ) + 2 cos ( θ 2 ) sin ( θ 2 )
= 1 + sin θ

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