Hi everyone:

Is there any way to prove the following identity:

tan(A/2)=(sinA)/(1+cosA)

without drawing a diagram? I know that it is a basic trig identity, but I don't know how to prove it by manipulating hte formulas.

Thanks!

Printable View

- Dec 20th 2009, 07:51 PMKelvinScaleProving a Trigonometric Identity
Hi everyone:

Is there any way to prove the following identity:

tan(A/2)=(sinA)/(1+cosA)

without drawing a diagram? I know that it is a basic trig identity, but I don't know how to prove it by manipulating hte formulas.

Thanks! - Dec 20th 2009, 08:30 PMbigwaveuse sin(x/2) / cos(x/2)

this derived from by using

in never negative, so the sign of the fractional expression depends only on the sign of - Dec 20th 2009, 08:36 PMSoroban
Hello, Kelvin!

We need these two identities: .

Quote:

Prove: .

Multiply by

. .

- Dec 20th 2009, 08:38 PMI-Think

Manipulating R.H.S.

Note that

Introduce into the equation and you should solve your problem

Edit

In the time I took to write this I was beaten by 2 other forum users

I really need to take typing classes.

On the other hand, at least I provided a different method - Dec 20th 2009, 08:41 PMKelvinScale
Thank you so much!

- Dec 20th 2009, 10:11 PMKelvinScale
Okay, Similar Question.

Prove that:

tan(A/2)=(1+sinA-cosA)/(1+sinA+cosA)

I tried replacing tan(A/2) with sinA/(1+cosA), but I could not find a way to add the extra components to both the numerator and denominator. Gosh this is frustrating. - Dec 21st 2009, 06:55 AMSoroban
Helolo, Kelvin!

This one is tricky . . .

Quote:

Prove: .

Multiply by

. .

. .

. .

. .

. .

. .

Multiply by

. . . . . . . . . . . . .

Finally: .

- Dec 21st 2009, 08:00 AMKrizalid
be careful with what angle you're working on, those identities are not true for all angles.