不等式スレッド
>227
Right = sin(a+b)/[2cos(a)cos(b)] = Middle/[2cos(a)cos(b)]{1+cos(a+b)}.
(Right - Middle)･[2cos(a)cos(b)] = Middle･[1+cos(a+b)-2cos(a)cos(b)] = Middle･[1-cos(a-b)] ≧0.
Left = tan(a+b)/2[1-tan(a)tan(b)].
Middle = tan(a+b)/2[1-tan{(a+b)/2}^2].
Middle^2 - Left^2 = 1 - 2tan{(a+b)/2}/tan(a+b) - [1 - {tan(a)+tan(b)}/tan(a+b)]
= {2/tan(a+b)}(Right - Middle).
Right = sin(a+b)/[2cos(a)cos(b)] = Middle/[2cos(a)cos(b)]{1+cos(a+b)}.
(Right - Middle)･[2cos(a)cos(b)] = Middle･[1+cos(a+b)-2cos(a)cos(b)] = Middle･[1-cos(a-b)] ≧0.
Left = tan(a+b)/2[1-tan(a)tan(b)].
Middle = tan(a+b)/2[1-tan{(a+b)/2}^2].
Middle^2 - Left^2 = 1 - 2tan{(a+b)/2}/tan(a+b) - [1 - {tan(a)+tan(b)}/tan(a+b)]
= {2/tan(a+b)}(Right - Middle).
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