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Math Help - C3 maths...please please help...

  1. #1
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    C3 maths...please please help...

    I'm having a complete mind blank..and can't do these two questions...

    any help would be greatly appreciated.

    1) By writing sin3x as sin (2x+x) show that sin 3x = 3sinx - 4sin(cubed)x

    i know that sin(2x+x) = sin2xcosx + cos2xsinx but i don't know where to go from there.

    2) f(x) = 1- 3 + 3 x does not = -2
    x+2 (x+2)squared

    show that f(x) = x(squared) + x + 1 x does not = -2
    (x+2)squared

    please help if you can do either of these.
    thanks
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  2. #2
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    Quote Originally Posted by Oranges&Lemons View Post
    I'm having a complete mind blank..and can't do these two questions...

    any help would be greatly appreciated.

    1) By writing sin3x as sin (2x+x) show that sin 3x = 3sinx - 4sin(cubed)x

    i know that sin(2x+x) = sin2xcosx + cos2xsinx but i don't know where to go from there.

    2) f(x) = 1- 3 + 3 x does not = -2
    x+2 (x+2)squared

    show that f(x) = x(squared) + x + 1 x does not = -2
    (x+2)squared

    please help if you can do either of these.
    thanks
    oops, number 2 didnt come out properly, the x+2 is supposed to be under the first 3 and the (x+2)squared is supposed to be under the second 3...and then the (x+2)squared is supposed to be under x(squared) + x + 1. sorry!
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Oranges&Lemons View Post
    1) By writing sin3x as sin (2x+x) show that sin 3x = 3sinx - 4sin(cubed)x

    i know that sin(2x+x) = sin2xcosx + cos2xsinx but i don't know where to go from there.
    You're almost there.
    sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x)

    And we know that
    sin(2x) = 2sin(x)cos(x)
    and
    cos(2x) = 1 - 2sin^2(x)
    and
    cos^2(x) = 1 - sin^2(x)

    You finish it from here.

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Oranges&Lemons View Post
    2) f(x) = 1- 3 + 3 x does not = -2
    x+2 (x+2)squared

    show that f(x) = x(squared) + x + 1 x does not = -2
    (x+2)squared
    Yes, the forum word processor doesn't like extra spaces does it?

    If I am reading this correctly it is:
    f(x) = 1 - \frac{3}{x + 2} + \frac{3}{(x + 2)^2}; x \neq -2

    and you need to show that
    f(x) = \frac{x^2 + x + 1}{(x + 2)^2}; x \neq -2

    I'm going to just drop the x \neq -2 part and just assume its there.

    So we've got
    f(x) = 1 - \frac{3}{x + 2} + \frac{3}{(x + 2)^2}

    Let's add the fractions. The LCM of 1, x + 2, (x + 2)^2 is, of course, (x + 2)^2, so
    f(x) = 1 \cdot \frac{(x + 2)^2}{(x + 2)^2} - \frac{3}{x + 2} \cdot \frac{x + 2}{x + 2}+ \frac{3}{(x + 2)^2}

    f(x) = \frac{(x + 2)^2 - 3(x + 2) + 3}{(x + 2)^2}

    See if you can finish this from here.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    Yes, the forum word processor doesn't like extra spaces does it?

    If I am reading this correctly it is:
    f(x) = 1 - \frac{3}{x + 2} + \frac{3}{(x + 2)^2}; x \neq -2

    and you need to show that
    f(x) = \frac{x^2 + x + 1}{(x + 2)^2}; x \neq -2

    I'm going to just drop the x \neq -2 part and just assume its there.

    So we've got
    f(x) = 1 - \frac{3}{x + 2} + \frac{3}{(x + 2)^2}

    Let's add the fractions. The LCM of 1, x + 2, (x + 2)^2 is, of course, (x + 2)^2, so
    f(x) = 1 \cdot \frac{(x + 2)^2}{(x + 2)^2} - \frac{3}{x + 2} \cdot \frac{x + 2}{x + 2}+ \frac{3}{(x + 2)^2}

    f(x) = \frac{(x + 2)^2 - 3(x + 2) + 3}{(x + 2)^2}

    See if you can finish this from here.

    -Dan
    thank you SO much! i really appreciate it
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