Question

sin(s-t)/sin(t) +cos(s-t)/cos(t)=sin(s)/sin(s)cos(t)

Answer 1

\[\frac{ \sin(s-t) }{ \sin t } + \frac{ \cos (s-t) }{ \cos t }=\frac{ \sin s }{ \sin s \cos t }\]

Answer 2

sure there is not a typo? i found the RHS should be =\[\frac{ \sin s }{ \sin t * \cos t }\]

Answer 3

ooops it was a typo but that's right

Answer 4

then the prob can be solved by using sin(A+B)=sinAcosB + cosAsinB and cos (A+B)=cosAcosB-sinAsinB

Answer 5

sin (s-t) = sin(s)cos(t) - cos(s)sin(t)
cos (s-t) = cos(s)cos(t) + sin(s)sin(t)

u can go on from here. good luck! :)

Answer 6

hmm you pretty much gonna need what @sdfgsdfgs use some algebra simplifying

Answer 7

\[\frac{\sin(s-t)}{\sin t}+\frac{\cos(s-t)}{\cos t}=\frac{\sin (s-t)\cos t+\sin t \cos (s-t)}{\sin t\cos t}\]

Answer 8

I got to that point and got stuck

Answer 9

realize that the top simplifies to sin (s-t +t)=sin(s)

Answer 10

that's all there is to it actually

Answer 11

So what am I simplifying?

Answer 12

you could treat s-t as x
so that it becomes obvious that sin(x)cost+sintcosx=sin(x+t)=sin(s-t+t)=sin(s)

Answer 13

see my last comment!

Answer 14

i went from left to right with the identity that @sdfgsdfgs has given you

Answer 15

Clear!

Answer 16

Ok i got it now

Answer 17

:) good!
you seem very new to OP
welcome to open study, enjoy the time you spend here

Answer 18

Yes I am! I enjoy coming here for help..thank you so much!