Deriving the half angle formula for Tangent

Some back story on this...
The motivation for this video came when I was trying to find a good source online to explain what happens to the plus/minus and absolute value sign in the formula and found NO GOOD SOURCES! I'm sure they are out there somewhere and probably in text books but I couldn't find it by googling and searching YouTube. I also checked my own website and the page on Trig derivations:

And I didn't fully explain it either!!! I glossed over the plus/minus and absolute value sign and didn't explain it completely.

Anyway, that's why I did the video and also updated my website.

The Trig cheat sheet on my website:

Some of the derivations including the half angle identities:

Website:

For more videos you can check out my OTHER channel:

For more great math videos check out Maths Plus!

#trigonometry
#trigonometryidentities

[ryanjohansson]

I was trying to derive the formula but was stuck after I got to the absolute value and plus/minus. Glad I found this video. Thanks!!

[mathsplus]

Very direct approach there with substituting in the x/2, really worked a treat. Thanks Owls School of Math 🙏🙏🙏❤💯

[abodamdfr]

Thanks for the video
It made me understand where did the +- go

[nid]

An other method for those who don’t want to remember the trig formulas is using the exponential form of cos and sin, you just then multiply the denominator by the conjugate, you simplify and you get it

[d.h.y]

You've already done the video at here xD So helpful🤓🤓

[prollysine]

Hi Owls ! proof of equality : u= (x/2) tan(x/2)=tan(u) = ---> (sinu*sinu)/(cosu*sinu) -> (sinu)^2/(sinu*cosu) -> -> (1-cos2u)/sin2u --> | u=(x/2) x=(2u) | --->>
-->> ||| (1-cosx)/sinx |||