Tangent of rational formula of half angle formula tana/2=sina/1+cosa=1-cosa/sina How did it come out?

tan(a/2)=sin(a/2)/cos(a/2)
Multiply 2 sin (A / 2)
=2sin^2(a/2)/[2sin(a/2)cos(a/2)]
According to the formula of double angle
=(1-cosa)/sina

The proof of half angle formula In triangle ABC, prove Sina / 2 = radical ((P-B) (P-C) / BC) Cosa / 2 = radical (P (P-A) / BC) Where p = (a + B + C) / 2 Help me

prove:
Cosine theorem
b^2+c^2-2*b*c*cosA=a^2
So: cosa = (b ^ 2 + C ^ 2-A ^ 2) / (2 * b * c)
Cosa = 1-2 * sin (A / 2) * sin (A / 2)
So: sin (A / 2) * sin (A / 2) = (1 - (b ^ 2 + C ^ 2-A ^ 2) / (2 * b * c)) = ((P-B) (P-C) / BC
Where p = (a + B + C) / 2
sin(A/2)=sqr((1-(b^2+c^2-a^2)/(2*b*c))=((p-b)(p-c)/bc)
cos(A/2)*cos(A/2)=1-sin(A/2)*sin(A/2)=(b^2+c^2-a^2)/(2*b*c)
cos(A/2)=sqr((b^2+c^2-a^2)/(2*b*c))=sqr(p(p-a)/bc)
Where p = (a + B + C) / 2

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Voiced consonants after vowels

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I'm an English teacher. I'd like to answer this question for you. 1. Both [i] and [e] in the international phonetic alphabet are pre vowels. The pronunciation characteristic of the front vowel is that the front of the tongue is moving. Generally, we divide the tongue into three parts: front, middle and back

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zhet
W, er, t
Er V
sheik

English pronunciation e. How to distinguish the pronunciation of "an, love"?

What exactly does it mean?
Generally, the pronunciation of a vowel depends on its collocation and syllables
For example, we is a syllable, and the sound of / E / is pronounced at this time; if it is a separate we, it will be pronounced / I: I: if we is a syllable/
In fact, English pronunciation is how to come, because the creation of their own language is people's casual speech, so read more can find the law, try it

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Send out
Antelope begins with a vowel

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C is the sound of [æ] and the rest is [EI]

Good morning, good afternoon, good evening in Spanish. How to pronounce it? How to say it when you answer the phone, how to write and how to say it? I want to learn Spanish by myself. Everyday language is OK. Who can give me some advice

buenos dias
buenas tardes
buenas noches
answer the phone...
All three of the above can be
S
dime
digame
buenos
hola
wait...

Tangent of rational formula of half angle formula tana/2=sina/1+cosa=1-cosa/sina How did it come out?