SOLUTION: Could you help me solve this problem? I need to prove the identity cos(u+v)cos(v)+sin(u+v)sin(v)= cos(u) Thank you!!!

Algebra ->  Trigonometry-basics -> SOLUTION: Could you help me solve this problem? I need to prove the identity cos(u+v)cos(v)+sin(u+v)sin(v)= cos(u) Thank you!!!      Log On


   

Question 769258: Could you help me solve this problem? I need to prove the identity
cos(u+v)cos(v)+sin(u+v)sin(v)= cos(u)
Thank you!!!
Found 2 solutions by lwsshak3, Edwin McCravy:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prove the identity
cos(u+v)cos(v)+sin(u+v)sin(v)= cos(u)
Use following identity:
cos(x-y)=cosxcosy+sinxsiny
cos(u+v)cos(v)+sin(u+v)sin(v)=cos((u+v)-v)=cos(u)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
cos(u+v)cos(v) + sin(u+v)sin(v) = cos(u)

Remembering the identity

cos(A-B) = cos(A)cos(B) + sin(A)sin(B)

we recognize that the left side,

cos(u+v)cos(v) + sin(u+v)sin(v)

is simply cos(A)cos(B) + sin(A)sin(B)

with u+v substituted for A and v substituted for B.

 we have

cos[(u+v)-v]

cos(u+v-v)

cos(u)

Edwin