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Math Help - compound angle formula problems

  1. #1
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    compound angle formula problems

    If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

    If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

    and

    If cosx + sinx = 2/3, find the value of sin 2x
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  2. #2
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    Quote Originally Posted by ringo View Post
    If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

    If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

    and

    If cosx + sinx = 2/3, find the value of sin 2x
    sin(x) = \frac{1}{2}sin(y) \: rightarrow \: 2sin(x) = sin(y)

    cos(x) = 3cos(y)

    sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

    Sub in the values you have for the above
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  3. #3
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    Quote Originally Posted by ringo View Post
    If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

    If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

    and

    If cosx + sinx = 2/3, find the value of sin 2x
    HI

    for the second part ,

    cos x + sin x =2/3

    square both sides , cos ^2 x + sin^2 x +2sin x cos x = 4/9

    2 sin x cos x = 4/9 -1
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