Prove the following identities.

Question

1. 1+cosx/1-cosx = secx + 1/secx -1
2. (tanx + cotx)^2=sec^2x csc^2x
3. cos(x+y) cos(x-y)= cos^2x - sin^2y

Answer 1

correction for #1, should say:

(1+cosx)/(1-cosx) = (secx + 1)/(secx - 1)

RS = (1/cosx + 1)/(1/cosx - 1)
= (1/cosx + 1)/(1/cosx - 1) * cosx/cox
= (1+ cosx)/(1 - cosx)
= LS
Well, that was easy.

#2, hint: change everything to sines and cosines
expand and simplify the LS

#3, use the expansion for cos(A ± B), multiply the result and watch what happens.
hint: remember a^4 - b^4 = (a^2+b^2)(a^2-b^2)