# Thread: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

1. ## prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

i have a couple of problem here that have been giving me trouble if you can solve any of them that would be great!!

Prove
1. sin3x=(sinx)(3-4sin^2x)

solve for all values in the interval (0-2pie)
2. sin3x=0

Prove
3. csc(x-y)= sec y/ sinx-cosx tany

2. ## Re: it stumped me

1. sin3x=(sinx)(3-4sin^2x)

Start by changing sin3x to sin(2x+x) then use the addition/subtraction identities and go from there. It worked out for me.

3. ## Re: it stumped me

yes i did that and then i did one more step but after that i just am getting really confused

4. ## Re: it stumped me

does anyone have any answers i really need them today. thanks so much

5. ## Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

sin3x=(sinx)(3-4sin^2x)

sin3x=
sin(2x+x)=
sin2x cosx + cos2x sinx =

Eliminate the "2x"s by using identities. Then get all in terms of sine only...eliminate cos[sup:1qy32vwv]2[/sup:1qy32vwv]x using cos[sup:1qy32vwv]2[/sup:1qy32vwv]x + sin[sup:1qy32vwv]2[/sup:1qy32vwv]x = 1.

6. ## Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

Originally Posted by bballbink
i have a couple of problem here that have been giving me trouble if you can solve any of them that would be great!!

Prove
1. sin3x=(sinx)(3-4sin^2x)

solve for all values in the interval (0-2pie)
2. sin3x=0

Prove
3. csc(x-y)= sec y/ sinx-cosx tany

7. ## Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

Prove
1. sin3x=(sinx)(3-4sin^2x)
sin(2x+x)
sin2x cosx+ cos2x sinx
?

solve for all values in the interval (0-2pie)
2. sin3x=0
sin(2x+x)
sin2x cosx+ cos2x sinx
?

Prove
3. csc(x-y)= sec y/ sinx-cosx tany

8. ## Re: prove sin3x=(sinx)(3-4sin^2x), solve sin3x=0, prove csc(x-y)

Originally Posted by bballbink
Prove
1. sin3x=(sinx)(3-4sin^2x)
sin(2x+x)
sin2x cosx+ cos2x sinx

What did you get following Loren's advice?

solve for all values in the interval (0-2pie)
2. sin3x=0
sin(2x+x)
sin2x cosx+ cos2x sinx
DUPLICATE POST

viewtopic.php?f=10&t=32901

Prove
3. csc(x-y)= sec y/ sinx-cosx tany

csc(x-y) = 1/sin(x-y)

Now continue.....

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