ยังงี้ปะคับ
$$\tan 75 \ =\ \frac{\sin (30+45)}{\cos (30+45)}$$
$$\ =\ \frac{\sin 30 \cos 45 + \sin 45 \cos 30}{\cos 30 \cos 45 - \sin 45 \sin 30}$$
$$\ =\ \frac{\frac{\sqrt 2}4 + \frac{\sqrt 2}2 \cdot \frac{\sqrt 3}2}{\frac{\sqrt 2}2 \cdot \frac{\sqrt 3}2 - \frac{\sqrt 2}4}$$
$$\ =\ \frac{\sqrt 2 + \sqrt 6}{\sqrt 6 - \sqrt 2}$$
$$\ =\ 2 + \sqrt 3$$
__________________
[[:://R-Tummykung de Lamar\\::]] ||
(a,b,c > 0,a+b+c=3)
$$\sqrt a+\sqrt b+\sqrt c\geq ab+ac+bc$$
|