Issolvi left(sin(30)right)^2left(cos(45)right)^2+4left(tan(30)right)^2+1/2left(sin(90)right)^2-2{left(cos(90)right)}^2+1/24{left(cos(0)right)}^2

$${ \left( \sin ( 30 ) \right) }^{ 2 } { \left( \cos ( 45 ) \right) }^{ 2 } +4 { \left( \tan ( 30 ) \right) }^{ 2 } + \frac{ 1 }{ 2 } { \left( \sin ( 90 ) \right) }^{ 2 } -2 { \left( \cos ( 90 ) \right) }^{ 2 } + \frac{ 1 }{ 24 } { \left( \cos ( 0 ) \right) }^{ 2 }$$

Evalwa

$$2$$

Passi tas-Soluzzjonijiet

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

$$\left(\frac{1}{2}\right)^{2}\left(\cos(45)\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ikkalkula \frac{1}{2} bil-power ta' 2 u tikseb \frac{1}{4}.

$$\frac{1}{4}\left(\cos(45)\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{1}{4}\times \left(\frac{\sqrt{2}}{2}\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{1}{4}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Immultiplika \frac{1}{4} b'\frac{\left(\sqrt{2}\right)^{2}}{2^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\times \left(\frac{\sqrt{3}}{3}\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Esprimi 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} bħala frazzjoni waħda.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ikseb il-valur ta’ \sin(90) mit-tabella tal-valuri trigonometriċi.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\times 1^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\times 1-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Immultiplika \frac{1}{2} u 1 biex tikseb \frac{1}{2}.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 4\times 2^{2} u 3^{2} huwa 144. Immultiplika \frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}} b'\frac{9}{9}. Immultiplika \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} b'\frac{16}{16}.

$$\frac{9\left(\sqrt{2}\right)^{2}}{144}+\frac{16\times 4\left(\sqrt{3}\right)^{2}}{144}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Billi \frac{9\left(\sqrt{2}\right)^{2}}{144} u \frac{16\times 4\left(\sqrt{3}\right)^{2}}{144} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{9\left(\sqrt{2}\right)^{2}+16\times 4\left(\sqrt{3}\right)^{2}}{144}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 4\times 2^{2} u 2 huwa 16. Immultiplika \frac{1}{2} b'\frac{8}{8}.

$$\frac{\left(\sqrt{2}\right)^{2}}{16}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{8}{16}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Billi \frac{\left(\sqrt{2}\right)^{2}}{16} u \frac{8}{16} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(\sqrt{2}\right)^{2}+8}{16}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3^{2} u 2 huwa 18. Immultiplika \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} b'\frac{2}{2}. Immultiplika \frac{1}{2} b'\frac{9}{9}.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}}{18}+\frac{9}{18}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Billi \frac{2\times 4\left(\sqrt{3}\right)^{2}}{18} u \frac{9}{18} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ikseb il-valur ta’ \cos(90) mit-tabella tal-valuri trigonometriċi.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\times 0^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ikkalkula 0 bil-power ta' 2 u tikseb 0.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\times 0+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Immultiplika 2 u 0 biex tikseb 0.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ikseb il-valur ta’ \cos(0) mit-tabella tal-valuri trigonometriċi.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\times 1^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\times 1$$

Immultiplika \frac{1}{24} u 1 biex tikseb \frac{1}{24}.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

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

$$\frac{2}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

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

$$\frac{2}{4\times 4}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

Immultiplika 4 u 4 biex tikseb 16.

$$\frac{2}{16}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

Naqqas il-frazzjoni \frac{2}{16} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{8}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

Immultiplika 2 u 4 biex tikseb 8.

$$\frac{1}{8}+\frac{8\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

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

$$\frac{1}{8}+\frac{8\times 3+9}{18}-0+\frac{1}{24}$$

Immultiplika 8 u 3 biex tikseb 24.

$$\frac{1}{8}+\frac{24+9}{18}-0+\frac{1}{24}$$

Żid 24 u 9 biex tikseb 33.

$$\frac{1}{8}+\frac{33}{18}-0+\frac{1}{24}$$

Naqqas il-frazzjoni \frac{33}{18} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{1}{8}+\frac{11}{6}-0+\frac{1}{24}$$

Żid \frac{1}{8} u \frac{11}{6} biex tikseb \frac{47}{24}.

$$\frac{47}{24}-0+\frac{1}{24}$$

Naqqas 0 minn \frac{47}{24} biex tikseb \frac{47}{24}.

$$\frac{47}{24}+\frac{1}{24}$$

Żid \frac{47}{24} u \frac{1}{24} biex tikseb 2.

$$2$$