Question

verify an identity of sin5xcos3x = sin4xcos4x + sinxcosx

Answer 1

I will post up what I know so far could you please check?

Answer 2

kk ;) !

Answer 3

yes ! The first step is correct @lsugano

Answer 4

But i dont know what to do next..><

Answer 5

kk sin(2x) =??!

Answer 6

That works
sin(8x) = sin(4x+4x) = 2sin(4x)cos(4x)

Answer 7

sin(8x)=sin(2(4x))=???

Answer 8

Looks like you are almost there just use: sin(2x) = 2sin(x)cos(x)

Answer 9

wait im really lost><

Answer 10

See the double angle formulas:
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 11

just Use the double angle formula ! for sin(2x) and sin(8x)

Answer 12

so like this: 8sinxcosx + 2sinxcosx ?

Answer 13

you're really lost : ) !
you had this ;
\[\sin(5x)\cos(3x)=\frac{1}{2}(\sin(\color{green}{8x})+\sin(\color{green}{2x}))\]

Answer 14

okay!

Answer 15

sin(8x)=...............(using the double angle formula....what we need to prove is something that contain 4x ....and we know that 8x=2(4x))

Answer 16

sin(2a)=2sin(a)cos(a)

Answer 17

why do we need to contain 4x?

Answer 18

\[\sin5xcos3x = \sin(\color{red}{4x})\cos(\color{red}{4x}) + \sin(x)\cos(x)\]

Answer 19

see now ?

Answer 20

you need to change sin(8x)=............
using sin(2a)=2sin(a)cos(a)

Answer 21

8/2 = 4 sin4a=4sin(a)cos(a)

Answer 22

no ! just focus ! sin(2a)=2sin(a)cos(a)
take a = 4x what will you get ?

Answer 23

2sin4xcos4x

Answer 24

yes ! now sin(2x)=......???

Answer 25

2sin2xcos2x

Answer 26

:'( !!! try again sin(2x)=......

Answer 27

2sinxcosx

Answer 28

yes ! Now can you finish this ?
using sin(8x)=2sin(4x)cos(4x) and sin(2x)=2sin(x)cos(x)
???

Answer 29

you add them right?

Answer 30

Maybe :) ! Just do what you have to do ! and I'll check :)

Answer 31

OHHH i got it okay i will write it on a tablet please check!!

Answer 32

kk ! Sure :)

Answer 33

Yeeeees ! that's correct :) !

Answer 34

ahh much more clear!!

Answer 35

:) ! just practice more ! And you'll be fine :)

Answer 36

so since 8x needed to be converted to the "sin2a" form, we divide 8xby2 and get 4x and we put a=4x correct?

Answer 37

yes ! keep in mind the double angle formula sin(2a)=2sin(a)cos(a)
or sin(something)=2sin(somthing/2)cos(something/2)

Answer 38

wonderful advice!! thank you very much! you're a teacher right? cuz your way better than the math teachers id had in the past!!

Answer 39

No ! I'm not a teacher !

Answer 40

oh wow ! thank you so much!

Answer 41

You're welcome ! Anytime :)