# C3 half angle of TAN proof!

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#1
If Sin1/2x= +/- (square root) ((1-cosx)/2)
and Cos1/2x= +/- (square root) ((1+cosx)/2)

Then how does tan1/2x become sinx/(1+cosx)?

Could someone explain the steps of the proof please. Thanks
0
5 years ago
#2
(Original post by Johnpeters)
If Sin1/2x= +/- (square root) ((1-cosx)/2)
and Cos1/2x= +/- (square root) ((1+cosx)/2)

Then how does tan1/2x become sinx/(1+cosx)?

Could someone explain the steps of the proof please. Thanks .

Then . Multiply top and bottom by .
1
#3
Thanks a lot EDIT: Don't you multiply the top and bottom by (squareroot) 1+cos(x)?
0
5 years ago
#4
good explanation.

just wondering why the "plus or minus" is not on the tan ?
0
5 years ago
#5
(Original post by Johnpeters)
Thanks a lot EDIT: Don't you multiply the top and bottom by (squareroot) 1+cos(x)?
Yes, sorry - I meant "multiply the fraction which is inside the square root", not "multiply the whole expression". Sorry.
0
5 years ago
#6
(Original post by the bear)
good explanation.

just wondering why the "plus or minus" is not on the tan ?
Consider when tan(x/2) is positive - it's exactly when x is between 0 and pi, or 2pi and 3pi, or…
Consider when sin(x) is positive - it's exactly when x is between 0 and pi, or 2pi and 3pi, or…
And 1+cos(x) is always positive.
0
5 years ago
#7
(Original post by Smaug123)
Consider when tan(x/2) is positive - it's exactly when x is between 0 and pi, or 2pi and 3pi, or…
Consider when sin(x) is positive - it's exactly when x is between 0 and pi, or 2pi and 3pi, or…
And 1+cos(x) is always positive.
thanks for that 0
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