Espressione goniometrica

TAN(135°)·(SIN(240°) - SIN(60°)) + TAN(240°)·(SIN(210°) - SIN(30°))=

=(-1)·(- √3/2 - √3/2) + √3·(- 1/2 - 1/2)=

=(-1)·(- √3) + √3·(-1)=

=√3 + (- √3) = 0

A) Ridurre al primo quadrante
* tg(135°) = tg(90° + 45°) = - 1/tg(45°)
* sin(240°) = sin(180° + 60°) = - sin(60°)
* tg(240°) = tg(180° + 60°) = tg(60°)
* sin(210°) = sin(180° + 30°) = - sin(30°)
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B) Sostituire, semplificare, consultare la tavola "Archi notevoli"
* (sin(240°) - sin(60°))*tg(135°) = (sin(210°) - sin(30°))*tg(240°) ≡
≡ (- sin(60°) - sin(60°))*(- 1/tg(45°)) = (- sin(30°) - sin(30°))*tg(60°) ≡
≡ 2*sin(60°)/tg(45°) = - 2*sin(30°)*tg(60°) ≡
≡ 2*√3/2 = - 2*√3/2 ≡
≡ √3 = - √3 ≡
≡ impossibile, perché √3 > 0
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C) Verificare con altri mezzi
http://www.wolframalpha.com/input?i=%28sin%28240%C2%B0%29-sin%2860%C2%B0%29%29*tg%28135%C2%B0%29%3D%28sin%28210%C2%B0%29-sin%2830%C2%B0%29%29*tg%28240%C2%B0%29