Respuesta :
From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).
How to prove trigonometric functions?
We want to prove that 1 - cot23° = 2/(1 - cot22°).
We will prove it using the trigonometric expression
cot(22° + 23°) = cot45°
Using trigonometric identities, we can rewrite as;
(cot22° cot23° - 1)/(cot22° + cot23°) = 1
Cross multiply to get;
cot22° cot23° - 1 = cot22° + cot23°
Rearrange to get;
cot22° cot23° - 1 - cot22° - cot23° =0
⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2
⇒ cot22° cot23° + 1 - cot22° - cot23° =2
⇒ cot22° cot23° - cot22° - cot23° + 1 = 2
⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2
⇒ (cot22° - 1) (cot23° - 1) = 2
Divide both sides by (cot23° - 1) to get;
cot23° - 1 = 2/(cot22° - 1)
⇒ 1 - cot23° = 2/(1 - cot22°).
Read more about trigonometric proof at; https://brainly.com/question/7331447
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