Prove the identity. (For Trigonometry)?

Question

Prove the identity.

cos(x - y) 1+ tan x tan y
------------ = ------------------
cos(x + y) 1- tan x tan y

here is the actual problem on the link below...thanks so much in advance for helping me.

http://www.fbixtreme.com/David/l1.jpg

Answer 1

okay,

cos(x-y) cos(x)*cos(y) + sin(x)*sin(y)
---------- = -----------------------------------
cos(x+y) cos(x)*cos(y) - sin(x)*sin(y)

(multiply and divide the fraction by cos(x)*cos(y))

1 + tan(x)*tan(y)
= ---------------------
1 - tan(x)*tan(y)

Answer 2

Find and use sum and difference formulas for cos and divide top and bottom by something to get that 1 out front.

Answer 3

LHS = Tan^2 a / (a million + tan^2 a) Tan = sin/cos, so =[Sin^2(a)/Cos^2(a)]/[a million+Sin^2(a)/cos^2... placed the expression on the bottom over a complication-loose denominator = [sin^2(a)/cos^2(a)]/[(cos^2(a)+sin^2(a))... sin^2 + cos^2 = a million, so = [sin^2(a)/cos^2(a)]/[a million/cos^2(a)] = sin^2(a)/cos^2(a) * cos^2(a)/a million = sin^2(a) = RHS