9
punti
Livello 0
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$\small \left(\cos\dfrac{\pi}{6}-\cos\dfrac{\pi}{4}\right)\left(\sin\dfrac{\pi}{3}+\sin\dfrac{\pi}{4}\right)-\tan^2\left(\dfrac{\pi}{3}\right)=$
$\small = \left(\cos30°-\cos45°\right)\left(\sin60°+\sin45°\right)-\tan^2\left(60°\right)=$
$\small = \left(\dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\right)\left(\dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\right)-\left(\sqrt3\right)^2 =$
$\small = \dfrac{3}{4}+\dfrac{\sqrt{3·2}}{4}-\dfrac{\sqrt{2·3}}{4}-\dfrac{\cancel2^1}{\cancel4_2}-3 =$
$\small = \dfrac{3}{4}+\cancel{\dfrac{\sqrt{6}}{4}}-\cancel{\dfrac{\sqrt{6}}{4}}-\dfrac{1}{2}-3 =$
$\small = \dfrac{3}{4}-\dfrac{1}{2}-3 =$
$\small = \dfrac{3-2-12}{4} =$
$\small = -\dfrac{11}{4} $
68268
punti
Genius I
@aurora_toch - Purtroppo non leggo bene il primo coseno, mi sembra $\small \cos\dfrac{\pi}{6}$, se così non fosse segui comunque il procedimento. Saluti.