Identies: Sum And Difference, Double Angle hurry

1. Mar 4, 2008

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

Last edited: Mar 4, 2008
2. Mar 4, 2008

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. Merely write 3x slightly differently so that the use of these identities becomes more evident.

3. Mar 4, 2008

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)

4. Mar 4, 2008

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??

5. Mar 4, 2008

jostpuur

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

6. Mar 4, 2008

emohunter7

okay thank you I will try that

7. Mar 4, 2008

emohunter7

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

8. Mar 4, 2008

emohunter7

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

9. Mar 4, 2008

cristo

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

10. Mar 4, 2008

emohunter7

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

11. Mar 4, 2008

jostpuur

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.

12. Mar 4, 2008

emohunter7

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

13. Mar 4, 2008

cristo

Staff Emeritus
Correct.

14. Mar 4, 2008

emohunter7

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

15. Mar 4, 2008

Cyrus

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

16. Mar 4, 2008

emohunter7

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

17. Mar 4, 2008

Cyrus

Ok, show some work now.

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

Last edited: Mar 4, 2008
18. Mar 5, 2008

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

19. Mar 5, 2008

Cyrus

Factor out a sin(x).

20. Mar 5, 2008

emohunter7

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