Issolvi cos(2*30^{circ})=1-tan^230^circ/1+tan^230^circ

$$\cos ( 2 \times 30 ^ { \circ } ) = \frac { 1 - \tan ^ { 2 } 30 ^ { \circ } } { 1 + \tan ^ { 2 } 30 ^ { \circ } }$$

Ivverifika

Passi tas-Soluzzjonijiet

Immultiplika 2 u 30 biex tikseb 60.

$$\cos(60)=\frac{1-\left(\tan(30)\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

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

$$\frac{1}{2}=\frac{1-\left(\tan(30)\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

Ikseb il-valur ta’ \tan(30) mit-tabella tal-valuri trigonometriċi.

$$\frac{1}{2}=\frac{1-\left(\frac{\sqrt{3}}{3}\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

Biex tgħolli \frac{\sqrt{3}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{1}{2}=\frac{1-\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}{1+\left(\tan(30)\right)^{2}}$$

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

$$\frac{1}{2}=\frac{1-\frac{3}{3^{2}}}{1+\left(\tan(30)\right)^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{1}{2}=\frac{1-\frac{3}{9}}{1+\left(\tan(30)\right)^{2}}$$

Naqqas il-frazzjoni \frac{3}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{1}{2}=\frac{1-\frac{1}{3}}{1+\left(\tan(30)\right)^{2}}$$

Naqqas \frac{1}{3} minn 1 biex tikseb \frac{2}{3}.

$$\frac{1}{2}=\frac{\frac{2}{3}}{1+\left(\tan(30)\right)^{2}}$$

Ikseb il-valur ta’ \tan(30) mit-tabella tal-valuri trigonometriċi.

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

Biex tgħolli \frac{\sqrt{3}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{3^{2}}{3^{2}}.

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

Billi \frac{3^{2}}{3^{2}} u \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Iddividi \frac{2}{3} b'\frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}} billi timmultiplika \frac{2}{3} bir-reċiproku ta' \frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}}.

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

Annulla 3 fin-numeratur u d-denominatur.

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

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{1}{2}=\frac{6}{\left(\sqrt{3}\right)^{2}+3^{2}}$$

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

$$\frac{1}{2}=\frac{6}{3+3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{1}{2}=\frac{6}{3+9}$$

Żid 3 u 9 biex tikseb 12.

$$\frac{1}{2}=\frac{6}{12}$$

Naqqas il-frazzjoni \frac{6}{12} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 6.

$$\frac{1}{2}=\frac{1}{2}$$

Qabbel \frac{1}{2} u \frac{1}{2}.

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