How do I show that \cos(t)+1=2\cos^2(\frac{t}{2}) I have been trying to

Reese Munoz

Reese Munoz

Answered question

2022-01-27

How do I show that cos(t)+1=2cos2(t2)
I have been trying to show that cos(t)+1 is equal to 2cos2(t2) Heres

Answer & Explanation

Flickkorbma

Flickkorbma

Beginner2022-01-28Added 17 answers

Notice that
cos(2α)=cos2αsin2α
Therefore, with α=t2 one has
cos(t)=cos2(t2)sin2(t2)
since sin2(t2)=1cos2(t2) one has the result.
ebbonxah

ebbonxah

Beginner2022-01-29Added 15 answers

Let f(t)=1+cost2cos2t2 and note that f(0)=0, f(0)=0 and ff

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