Identies: Sum And Difference, Double Angle hurry

[emohunter7]

I need some help with these kind of problems. I don't clearly understand how to solve them. Here is one...PLEASE HELP!

sin 3x = (sin x)(3-4sin^2 x) PROVE THEY ARE EQUAL

 

[jostpuur]

I need some help with these kind of problems. I don't clearly understand how to solve them. Here is one...PLEASE HELP!

sin 3x = (sin x)(3-4sin^2 x) PROVE THEY ARE EQUAL

You can use identities sin(x+y) = cos(x)sin(y) + sin(x)cos(y) and sin(2x) = 2sin(x)cos(x) for this. Merely write 3x slightly differently so that the use of these identities becomes more evident.

 

[emohunter7]

thank you...alright this one i am stuck on...i have been working on it for 10 minutes and can't come up with the answer.
2csc2x=(csc^2x)(tanx)

 

[emohunter7]

would the correct answer for my first problem be:
change sin3x to (sinx)(sin2x)
then change sin2x to 2sinxcosx
then change that to (2sinx)(2-2sinx)
then...i don't know...but am I on the right track??

 

[jostpuur]

change sin3x to (sinx)(sin2x)

This is incorrect. Put sin(3x) = sin(x + 2x) instead.

 

[emohunter7]

okay thank you I will try that

 

[emohunter7]

alright as my next step I put (sinx)(cos2x)+(sin2x)(cosx)...is this correct?

 

[emohunter7]

do I then change the cos's to sin's?

 

[cristo]

alright as my next step I put (sinx)(cos2x)+(sin2x)(cosx)...is this correct?

Yes. Perhaps you should attempt the entire problem and then post your solution instead of posting line by line.

 

[emohunter7]

sorry I just need to know where I'm messing up.

 

[jostpuur]

You can use identities sin(x+y) = cos(x)sin(y) + sin(x)cos(y) and sin(2x) = 2sin(x)cos(x) for this.

do I then change the cos's to sin's?

Okey, my first advice wasn't flawless because I didn't notice that you need the formula for cos(2x) too. You cannot switch sines to cosines arbitrarily.

 

[emohunter7]

so by using cos2x and sin2x formulas I should get (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)...right??

 

[cristo]

so by using cos2x and sin2x formulas I should get (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)...right??

Correct.

 

[emohunter7]

then do I multiply the (2sinxcosx)(cosx) ?

 

[Cyrus]

Rewrite what your problem is and what you want to solve starting from the beginning please.

 

[emohunter7]

the problem is:
sin3x = (sinx)(3-4sin^2 x) ...PROVE THAT THEY ARE EQUAL

 

[Cyrus]

Ok, show some work now.

(Im going to bed in 10 min, so type fast if you want help).

 

[emohunter7]

ok...
first i split sin3x making sin(x+2x)
than i used the sum identity making (sinx)(cos2x)+(sin2x)(cosx)
then i used double angle identity making (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)
dunno what to do next

 

[Cyrus]

Factor out a sin(x).

 

[emohunter7]

i got it :) thanks!
new homework... will you help me with it if I have trouble?

 

[Tedjn]

Feel free to post your question and your work on it.

 

[emohunter7]

okay thank you