Find the exact value by using a half-angle identity; tan(7pi/8)

Question

anonymous · Answer

@Jhannybean What do you think?

anonymous · Answer

@Luigi0210  I sure could use your brain right about now as well...

luigi0210 · Answer

What is the half-angle formula again?

anonymous · Answer

@Luigi0210  Um..it's kinda difficult to put on here but I'll try. 

sin: sin x/2 = +-sqrt1-cos(x)/2

luigi0210 · Answer

isn't it tan?

anonymous · Answer

cos: cos x/2 = +-sqrt1+cos(x)/2

tan: tan x/2 = 1-cos(x)/sin(x)

luigi0210 · Answer

There you go

luigi0210 · Answer

Well I got $$\sqrt{2}-1$$

anonymous · Answer

Really? Huh x) I've seen so many fractions today I nearly forgot about the possiblilty of a whole number (if that classifies as one)

luigi0210 · Answer

I might be wrong.. but do you understand how I arrived at that answer?

anonymous · Answer

Not really, could you explain?

luigi0210 · Answer

and btw I was wrong it's $$1-\sqrt{2}$$

luigi0210 · Answer

and sure hold on

luigi0210 · Answer

$$\tan \frac{ \theta }{ 2 }=\frac{ 1-\cos \theta }{ \sin \theta } $$
$$\tan \frac{ (\frac{ 7\Pi }{ 4 }) }{ 2 }=\frac{ 1-\cos \frac{ 7\Pi }{ 4 } }{ \sin \frac{ 7\Pi }{ 4 } }$$

luigi0210 · Answer

can you figure it out from here?

anonymous · Answer

lol no, I'm horrible at this stuff, I just want to finish my last couple of tests and be done with this class

luigi0210 · Answer

Ah alright well I'm here if you need anything buddy