trigonometry

Show that (cosð + cosß)² + (sinð + sinß)² = 4cot(ð-ß/2)

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  1. I will write it as:
    (cosx + cosy)² + (sinx + siny)² = 4cot(x-y/2) --> easier to type

    LS = cos^2 x + 2cosxcosy + cos^2 y + sin^2 x + 2sinxsiny + sin^2 x
    = sin^2 x + cos^2 x + sin^ y + cos^2 y + 2(cosxcosy + sinxsiny)
    = 2 + 2cos(x - y)
    = 2(1 + cos(x-y) )

    RS = 4 cot(x - y/2)
    = 4(1 + tanxtan y/2)/(tanx - tan y/2)
    = ........

    see what you can do with that.

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  2. If that fails, try cot (x-y)/2
    and use your half-angle formula, and more parentheses next time.

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  3. ahh, the old "missing bracket" trap.
    Thanks Steve.

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