Which of the following are identities? Check all that apply A. Tan(x-pi)=tanx B. Cos(x+y) – cos(x-y)= 2cosxcosy C. Cos(x+y) +cos(x-y)= 2 cosxcosy D. Sin(x+y) +sin (x-y)= 2cosxsiny
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A and C are identities.
A. `tan(x-pi)=(tanx-tanpi)/(1+tanxtanpi)=(tanx)/1=tanx`
B. `cos(x+y)-cos(x-y)`
`=cosxcosy-sinxsiny-[cosxcosy+sinxsiny]`
`=-2sinxsiny`
C. `cos(x+y)+cos(x-y)`
`=cosxcosy-sinxsiny+cosxcosy+sinxsiny`
`=2cosxcosy`
D. `sin(x+y)+sin(x-y)`
`=sinxcosy+cosxsiny+sinxcosy-cosxsiny`
`=2sinxcosy`
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