Issolvi (2-sqrt{3})*tan60^circ+tan45^circ/1-tan60^circtan45^circ

$$( 2 - \sqrt { 3 } ) \cdot \frac { \tan 60 ^ { \circ } + \tan 45 ^ { \circ } } { 1 - \tan 60 ^ { \circ } \tan 45 ^ { \circ } }$$

Evalwa

$$-1$$

Passi tas-Soluzzjonijiet

Ikseb il-valur ta’ \tan(60) mit-tabella tal-valuri trigonometriċi.

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+\tan(45)}{1-\tan(60)\tan(45)}$$

Ikseb il-valur ta’ \tan(45) mit-tabella tal-valuri trigonometriċi.

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\tan(60)\tan(45)}$$

Ikseb il-valur ta’ \tan(60) mit-tabella tal-valuri trigonometriċi.

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\tan(45)}$$

Ikseb il-valur ta’ \tan(45) mit-tabella tal-valuri trigonometriċi.

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\times 1}$$

Esprimi \left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\times 1} bħala frazzjoni waħda.

$$\frac{\left(2-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{1-\sqrt{3}\times 1}$$

Uża l-propjetà distributtiva biex timmultiplika 2-\sqrt{3} b'\sqrt{3}+1 u kkombina termini simili.

$$\frac{\sqrt{3}+2-\left(\sqrt{3}\right)^{2}}{1-\sqrt{3}\times 1}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{\sqrt{3}+2-3}{1-\sqrt{3}\times 1}$$

Naqqas 3 minn 2 biex tikseb -1.

$$\frac{\sqrt{3}-1}{1-\sqrt{3}\times 1}$$

Estratta l-sinjal negattiv fi \sqrt{3}-1.

$$\frac{-\left(-\sqrt{3}+1\right)}{-\sqrt{3}+1}$$

Annulla -\sqrt{3}+1 fin-numeratur u d-denominatur.

$$-1$$