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    

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team