Question

Thanks for helping!


6. Prove the identity:
(cosx+cosy)^2+(sinx-siny)^2=2+2cos(x+y)
Part I: Complete the left-hand column of the table below following the steps indicated in the right-hand column. (12 points)
Given on the left side of the original problem
(cosx+cosy)^2+(sinx-siny)^2

Expand each squared term



Simplify the expression



Apply the Pythagorean identity



Apply the addition formula for cosine

Answer 1

@dan815 @Kainui @jim_thompson5910 @zepdrix

Answer 2

expand left side

Answer 3

(cosx+cosy)^2+(sinx-siny)^2=??

Answer 4

2+2cos(x+y)

Answer 5

no i mean expand it

Answer 6

oh
gotcha

Answer 7

and use the cos trig identities

Answer 8

cosxcosy+sinxsiny = cos(x+y) ?

Answer 9

cos^2(x)+2cos(x)cos(y)-2sin(x)sin(x)+cos^2(x)+sin^2(y)+sin^2

Answer 10

That is the identity?

Answer 11

i dunno maybe its a negative inbetween

Answer 12

cosxcosy- sinxsiny = cos(x+y) ?

Answer 13

http://prntscr.com/7daa8n

Answer 14

check it out

Answer 15

thanks, from here I can simplify and use the Pythagorean identity?

Answer 16

yep

Answer 17

sin^2(a) + cos^2(a) = 1;