Question

true or false
sinx cosy = 1/2(sin(x+y)+ cos(x-y))
answer with explaination please

Answer 1

sin(x+y) = sin(x)cos(y) + sin(y)cos(x)
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

can you answer now ?

Answer 2

its true becuase 1/2 of 2 sinxcosy is that?

Answer 3

show me .. use the formulas that i gave and show me that the right side equal the left side
if it's true you should be able to show it

Answer 4

er ..i kinda got it in my head ..i just can't put in on paper ...can you help me ._.

Answer 5

sinx cosy = 1/2(sin(x)cos(y) + sin(y)cos(x)+ cos(x)cos(y) + sin(x)sin(y))

Answer 6

try working with this now

Answer 7

her ..multiply by 2 on both sides?

Answer 8

ok

Answer 9

try manipulating it ..
do you think it is true ?

Answer 10

are you there ?

Answer 11

yeah sorry im uh trying ..but confused alittle

Answer 12

if you cant show that the right side is equal to the left side after manipulating
it might be false!

in fact we can show that this is false by choosing x=0 and y=0 and put it in the original equation :

sinx cosy = 1/2(sin(x+y)+ cos(x-y))

sin0cos0 = 1/2(sin0 + cos0)
0 = 1/2(0 + 1)
0 = 1/2

false!

Answer 13

oh ._. i got it backwards

Answer 14

note that in order to show that this is true we cant just choose numbers
we really have to manipulate the original equation and see that the left side equals the right side

but if we want to show that it is false choosing two values is enough!

Answer 15

oh okay
ty