Issolvi frac{5sin^{2}30^{circ}+cos^{2}45^{circ}-4tan^{2}30^circ}{2sec60^circ*sin30^circ+tan45^circ}

$$\frac { 5 \sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ } - 4 \tan ^ { 2 } 30 ^ { \circ } } { 2 \sec 60 ^ { \circ } \times \sin 30 ^ { \circ } + \tan 45 ^ { \circ } }$$

Evalwa

$$\frac{1250000000000000}{9928203230275509}\approx 0.12590395$$

Passi tas-Soluzzjonijiet

Evaluate trigonometric functions in the problem

$$\frac{5 \sin^{2}(30) + \cos^{2}(45) - 4 \tan^{2}(30)}{2 \cdot 1.1547005383792515 + \tan(45)}$$

Get the value of \sin(30) from trigonometric values table.

$$\frac{5\times \left(\frac{1}{2}\right)^{2}+\left(\cos(45)\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{5\times \frac{1}{4}+\left(\cos(45)\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

Immultiplika 5 u \frac{1}{4} biex tikseb \frac{5}{4}.

$$\frac{\frac{5}{4}+\left(\cos(45)\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

Get the value of \cos(45) from trigonometric values table.

$$\frac{\frac{5}{4}+\left(\frac{\sqrt{2}}{2}\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Espandi 2^{2}.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{4}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

Billi \frac{5}{4} u \frac{\left(\sqrt{2}\right)^{2}}{4} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\left(\tan(30)\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

Get the value of \tan(30) from trigonometric values table.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\times \left(\frac{\sqrt{3}}{3}\right)^{2}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4\times 3}{3^{2}}}{2\times 1.1547005383792515+\tan(45)}$$

Immultiplika 4 u 3 biex tikseb 12.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{12}{3^{2}}}{2\times 1.1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{12}{9}}{2\times 1.1547005383792515+\tan(45)}$$

Naqqas il-frazzjoni \frac{12}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4}{3}}{2\times 1.1547005383792515+\tan(45)}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 4 u 3 huwa 12. Immultiplika \frac{5+\left(\sqrt{2}\right)^{2}}{4} b'\frac{3}{3}. Immultiplika \frac{4}{3} b'\frac{4}{4}.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)}{12}-\frac{4\times 4}{12}}{2\times 1.1547005383792515+\tan(45)}$$

Billi \frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)}{12} u \frac{4\times 4}{12} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2\times 1.1547005383792515+\tan(45)}$$

Immultiplika 2 u 1.1547005383792515 biex tikseb 2.309401076758503.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2.309401076758503+\tan(45)}$$

Get the value of \tan(45) from trigonometric values table.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2.309401076758503+1}$$

Żid 2.309401076758503 u 1 biex tikseb 3.309401076758503.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3.309401076758503}$$

Esprimi \frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3.309401076758503} bħala frazzjoni waħda.

$$\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12\times 3.309401076758503}$$

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

$$\frac{3\left(5+2\right)-4\times 4}{12\times 3.309401076758503}$$

Żid 5 u 2 biex tikseb 7.

$$\frac{3\times 7-4\times 4}{12\times 3.309401076758503}$$

Immultiplika 3 u 7 biex tikseb 21.

$$\frac{21-4\times 4}{12\times 3.309401076758503}$$

Immultiplika -4 u 4 biex tikseb -16.

$$\frac{21-16}{12\times 3.309401076758503}$$

Naqqas 16 minn 21 biex tikseb 5.

$$\frac{5}{12\times 3.309401076758503}$$

Immultiplika 12 u 3.309401076758503 biex tikseb 39.712812921102036.

$$\frac{5}{39.712812921102036}$$

Espandi \frac{5}{39.712812921102036} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'1000000000000000.

$$\frac{5000000000000000}{39712812921102036}$$

Naqqas il-frazzjoni \frac{5000000000000000}{39712812921102036} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 4.

$$\frac{1250000000000000}{9928203230275509}$$