Question

Arătaţi că sin 30°cos 30° + 2 sin 45ºcos 45º -sin 60°cos 60° =1.
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Answer 1

$\frac{1}{2} \frac{\sqrt{3}}{2} +2\frac{\sqrt{2}}{2} \frac{\sqrt{2}}{2} -\frac{\sqrt{3}}{2} \frac{1}{2} =\\\frac{\sqrt{3}}{4} +2*\frac{2}{4} -\frac{\sqrt{3}}{4}=\\=\frac{2*2}{4} =1$

Answer 2

Explicație pas cu pas:

sin30°=1/2 cos30°=√3/2 sin45°=1/√2 cos45°=√2/2 sin60°=√3/2 cos60°=1/2

1/2×√3/2+2×1/√2×√2/2 -√3/2 ×1/2=1