Anonymous
Anonymous asked in Science & MathematicsMathematics · 10 years ago

prove that sin(a+b+c)= sina+cosb+cosc+sinb+cosa+cosc+sinc+cosb+cosa-sina-sinb-sinc?

thanx

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  • 10 years ago
    Favourite answer

    Use the formula

    sin(a + b) = sina cosb + sinb cos a

    Then sin(a + b + c)

    = sin((a + b) + c)

    = sin(a + b) cosc + cos(a + b) sin c

    Then use the formula

    cos(a + b) = cosa cosb - sina sinb to get

    sin(a + b) cosc + cos(a + b) sin c

    = (sina cosb + sinb cosa) cosc + (cosa cosb - sina sinb) sinc

    = sina cosb cosc + sinb cosa cosc + sinc cosa cosb - sina sinb sinc

  • 10 years ago

    you seem to be missing a bit, but what, for instance does sin (x+y) equal, in terms of x and y?

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