Question

Verify cos(a+b)/cos(a-b)=1-tan(a)tan(b)/1+tan(a)tan(b)

Answer 1

See if you follow this. reference line numbers for explanations, if necessary.

Answer 2

Line 1: sum/diff identities for cosine
Line 2: mutltiply by 1 in the form of the reciprocal of cos(a)cos(b) over itself; this give the ! in numerator and denominator
Line 3: cancellation property of algebra
Line 4: Quotient property tan(a) = sin(a)/cos(a)

Answer 3

@gryphon i don't know how do this... can you start it a bit for me? This is extremely difficult.

Answer 4

I just did it (see the pdf in my first post-- did you not see it?); and I explained it line by line in the second post.

Answer 5

oooh sorry, i've been at this the entire day haha

Answer 6

thanks a lot, you're saving me here

Answer 7

do you need any more explanation of the line by line?

Answer 8

The key to this is line 2 where you force the required terms to become 1.

Answer 9

ah ok, i didn't understand how to get to that second line

Answer 10

Also going from line 1 to line 2, you have to commute the terms of the denominator

Answer 11

I have this other problem, it's 2tan(x/2) = sin^2x+1-cos^2x/sinx(1+cosx)

Answer 12

and again thank you very much, i've had to do like 15 of these and they're all incredibly hard but these 2 have been impossible

Answer 13

np, please double check that you entered the identity correctly before I try. thanks

Answer 14

It's 2tan(x/2) = sin^2 x+1-cos^2 x / sinx(1+cosx)

That's what it says on the paper.

Answer 15

ok, i think i have something close... give me a minute

Answer 16

ok, I got it, give me a second to clean it up and post it

Answer 17

wow thanks, i really appreciate you taking your time to do this.

Answer 18

np! these aren't that hard once you get the hang of it. you just have to keep at it!

Answer 19

u good?

Answer 20

yep, i have 2 questions left that have to do with 0,2pi intervals. could you help me with that? No problem if you have to go you've done enough for me already.

Answer 21

sorry, I would have liked to help, but I logged out before reading your last post.