Prove the following identities.
1. 1+cosx/1cosx = secx + 1/secx 1
2. (tanx + cotx)^2=sec^2x csc^2x
3. cos(x+y) cos(xy)= cos^2x  sin^2y
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1 answer

correction for #1, should say:
(1+cosx)/(1cosx) = (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^2b^2) 👍
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