Issolvi frac{1-sin^{2}45^{circ}}{1+sin^245^circ}+tan^245^circ

$$\frac { 1 - \sin ^ { 2 } 45 ^ { \circ } } { 1 + \sin ^ { 2 } 45 ^ { \circ } } + \tan ^ { 2 } 45 ^ { \circ }$$

Evalwa

$$\frac{4}{3}\approx 1.333333333$$

Passi tas-Soluzzjonijiet

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

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

Biex tgħolli \frac{\sqrt{2}}{2} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{1-\frac{2}{2^{2}}}{1+\left(\sin(45)\right)^{2}}+\left(\tan(45)\right)^{2}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{1-\frac{2}{4}}{1+\left(\sin(45)\right)^{2}}+\left(\tan(45)\right)^{2}$$

Naqqas il-frazzjoni \frac{2}{4} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1-\frac{1}{2}}{1+\left(\sin(45)\right)^{2}}+\left(\tan(45)\right)^{2}$$

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

$$\frac{\frac{1}{2}}{1+\left(\sin(45)\right)^{2}}+\left(\tan(45)\right)^{2}$$

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

$$\frac{\frac{1}{2}}{1+\left(\frac{\sqrt{2}}{2}\right)^{2}}+\left(\tan(45)\right)^{2}$$

Biex tgħolli \frac{\sqrt{2}}{2} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{\frac{1}{2}}{1+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}+\left(\tan(45)\right)^{2}$$

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

$$\frac{\frac{1}{2}}{\frac{2^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}+\left(\tan(45)\right)^{2}$$

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

$$\frac{\frac{1}{2}}{\frac{2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}}+\left(\tan(45)\right)^{2}$$

Iddividi \frac{1}{2} b'\frac{2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}} billi timmultiplika \frac{1}{2} bir-reċiproku ta' \frac{2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}.

$$\frac{2^{2}}{2\left(2^{2}+\left(\sqrt{2}\right)^{2}\right)}+\left(\tan(45)\right)^{2}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{2}{\left(\sqrt{2}\right)^{2}+2^{2}}+\left(\tan(45)\right)^{2}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{2}{2+2^{2}}+\left(\tan(45)\right)^{2}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{2}{2+4}+\left(\tan(45)\right)^{2}$$

Żid 2 u 4 biex tikseb 6.

$$\frac{2}{6}+\left(\tan(45)\right)^{2}$$

Naqqas il-frazzjoni \frac{2}{6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{3}+\left(\tan(45)\right)^{2}$$

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

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

Ikkalkula 1 bil-power ta' 2 u tikseb 1.

$$\frac{1}{3}+1$$

Żid \frac{1}{3} u 1 biex tikseb \frac{4}{3}.

$$\frac{4}{3}$$