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Need help with simple double angles

is cos x= 1-sin^2 (x/2) or cos(x)=1-2sin^2 (x/2)
Reply 1
Avatar for Zacken
Zacken
22
Original post by jeja12
is cos x= 1-sin^2 (x/2) or cos(x)=1-2sin^2 (x/2)


The latter.

cos x = 1 - 2sin^2 (x/2)
Reply 2
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jeja12
OP
1
Thank you, looks like I had it wrong in my notes after all
Reply 3
Avatar for Alexion
Alexion
17
I tend to remember them the other way round, easier that way:

cos2x = 1/2 + 1/2cos2x

sin2x = 1/2 - 1/2cos2x
Reply 4
Avatar for Zacken
Zacken
22
Original post by jeja12
Thank you, looks like I had it wrong in my notes after all


The easiest one to remember is cos 2x = cos^2 x - sin^2 x

and then you can derive the others from that by replacing cos^2 x with 1 - sin^2 x or sin^2 x with 1 - cos^2 x.
Reply 5
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jeja12
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1
Could you confirm my notes are correct since im really confused by the sin(3x) and the proof
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IMG_1239.jpg529.8KB
Reply 6
Avatar for Zacken
Zacken
22
Original post by jeja12
Could you confirm my notes are correct since im really confused by the sin(3x) and the proof


They are correct.
SinX= 2Sin[X/2]Cos[X/2]

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