Question

Please help
Prove the following
(sin(3x)+sin(x))/(sin(3x)-sin(x)=2/(1-tan^2(x))

Answer 1

So far by using addition identities I got to -2/(2tan2(x)-sec^2(x))

Answer 2

\(\bf \cfrac{sin(3x)+sin(x)}{sin(3x)-sin(x)}=\cfrac{2}{1-tan^2(x)}?\)

Answer 3

question:
are you allowed to use the following two identities:
\[\sin(\alpha)+\sin(\beta)=2 \sin(\frac{\alpha+\beta}{2})\cos(\frac{\alpha-\beta}{2}) \\ \sin(\alpha)-\sin(\beta)=2 \cos(\frac{\alpha+\beta}{2})\sin(\frac{\alpha-\beta}{2})\]
if not I will go ahead and check by addition identities that I can get to what you have ?

Answer 4

Yes @jdoe0001
And I am not allowed to use those @myininaya

Answer 5

hmmm I'm not getting that expression after using those sum identities
but that doesn't mean what you have is wrong
let's assume it is right
try writing sec^2(x) in terms of tan^2(x) using one of the Pythagorean identities

Answer 6

Alright
I'll try that

Answer 7

yep it looks like you were almost there

Answer 8

Wow I was really close

Answer 9

Thanks a lot! :)

Answer 10

But just to make sure we just multiply by -1/-1 at the end to get the one on the RHS right?

Answer 11

yep

Answer 12

k thanks! :)

Answer 13

You use that Pythagorean identity I mentioned
collect like terms on bottom
then last step multiply by -1/-1

Answer 14

np