Question

Simplify [sin(s-t)/sin t] + [cos (s-t)/cos t] to sin s/ (sin s cos t)

I used the identity of both but I can't seem to get rid of any of the functions

Answer 1

\[\frac{\sin(s-t)}{sint}+\frac{\cos(s-t)}{cost}=\frac{sins*cost-sint*coss}{sint}+\frac{coss*cost+sins*sint}{cost}\]
=\[\frac{sins*cost}{sint}-\frac{sint*cost}{sint}+\frac{coss*cost}{cost}+\frac{sins*sint}{cost}\]
=\[\frac{sins*cost}{sint}-cost+cost+\frac{sins*sint}{cost}\]
=\[\frac{cost(sins*cost)+sint(sins*sint)}{sint*cost}=\frac{sins(\cos^2t+\sin^2t)}{sintcost}=\frac{sins}{sintcost}\]

Answer 2

any questions?

Answer 3

what happened to the sins in the last step? It should be a 2sins by the way I interpreted it\[sins(\cos^2t)+sins(\sin^2t)=2sins(\cos^2t+\sin^2t)\]

Answer 4

where did you get 2?

Answer 5

do you know how to factor?

Answer 6

xy+xz does not equal 2x(y+z)
xy+xz=x(y+z)

Answer 7

oh, my goodness, I don't know why that wasn't obvious to me, but its very clear now. I get all of it. Really appreciate the help, Thanks!

Answer 8

lol
and you know that cos^2x+sin^2x=1 right?
if you want to give me a medal thats cool lol

Answer 9

yeah, the best identity there is!! haha. If you could point out how to do that, I will. Also, I don't know how to close this question as "Has a good answer"

Answer 10

^^^^^^^^^
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the button is here

Answer 11

i've clicked on the blue thing, your icon and the actual medal, nothing happens, I'm new here, like today new, if that matters.

Answer 12

its cool no worries

Answer 13

its above the word delete

Answer 14

I see theres a good answer button in other open study windows I have, but not this window. I'll be asking help again sometime, and hopefully the button reappears by then lol.

Answer 15

lol you did it!
you get a medal for that

Answer 16

there we go, just refreshed the page lol. Thanks!