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How is it simplified into cos(x)+1? What identity am I missing out?
clauirizarry
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2cos^(2)(x/2)
Add 0 in the form of (-1 + 1):
2cos^(2)(x/2) - 1 + 1
Use double angle formula with the first two terms.
We know cos(2x) = 2cos^(2)(x) - 1
cos(2•x/2) + 1
cos(x) + 1
ZeeshanZaidi
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Use the half angle formula cos x/2 = ± sqrt( ( 1 + cos x ) / 2 ).
AzeemVictor
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Use cos(x) = 2 cos(x/2)\^2 – 1 ,
which follows from applying the Pythagorean identity to
cos(x) = cos(x/2)\^2 - sin(x/2)\^2 ,
which follows from the cosine addition formula.
ad_sampson
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I always just skip to Euler and use cos(x) = (e\^(ix) +e\^(-ix))/2.
​
It's pretty straightforward to substitute that expression in for cosine and square it to derive the answer.
wearehightyde
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Just cos
IanKenyonNFL
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IanKenyonNFL
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Cos(2x) = 2cos²x - 1,
For half angel that will be
cos(x) = 2cos²(x/2) - 1 ,
Rearranging terms
2cos²(x/2) = cos(x) + 1
prichard_3
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