Riješi 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

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

Procijeni

$$2$$

Koraci za rješenje

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

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

Izračunajte \frac{1}{2} stepen od 2 i dobijte \frac{1}{4}.

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

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

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

Da biste podigli \frac{\sqrt{2}}{2} na potenciju, dignite brojnik i nazivnik na potenciju i zatim podijelite.

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

Pomnožite \frac{1}{4} i \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

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

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

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

Da biste podigli \frac{\sqrt{3}}{3} na potenciju, dignite brojnik i nazivnik na potenciju i zatim podijelite.

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

Izrazite 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} kao jedan razlomak.

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

Get the value of \sin(90) from trigonometric values table.

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

Izračunajte 1 stepen od 2 i dobijte 1.

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

Pomnožite \frac{1}{2} i 1 da biste dobili \frac{1}{2}.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva 4\times 2^{2} i 3^{2} je 144. Pomnožite \frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}} i \frac{9}{9}. Pomnožite \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} i \frac{16}{16}.

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

Pošto \frac{9\left(\sqrt{2}\right)^{2}}{144} i \frac{16\times 4\left(\sqrt{3}\right)^{2}}{144} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva 4\times 2^{2} i 2 je 16. Pomnožite \frac{1}{2} i \frac{8}{8}.

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

Pošto \frac{\left(\sqrt{2}\right)^{2}}{16} i \frac{8}{16} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva 3^{2} i 2 je 18. Pomnožite \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} i \frac{2}{2}. Pomnožite \frac{1}{2} i \frac{9}{9}.

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

Pošto \frac{2\times 4\left(\sqrt{3}\right)^{2}}{18} i \frac{9}{18} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Get the value of \cos(90) from trigonometric values table.

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

Izračunajte 0 stepen od 2 i dobijte 0.

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

Pomnožite 2 i 0 da biste dobili 0.

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

Get the value of \cos(0) from trigonometric values table.

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

Izračunajte 1 stepen od 2 i dobijte 1.

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

Pomnožite \frac{1}{24} i 1 da biste dobili \frac{1}{24}.

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

Kvadrat broja \sqrt{2} je 2.

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

Izračunajte 2 stepen od 2 i dobijte 4.

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

Pomnožite 4 i 4 da biste dobili 16.

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

Svedite razlomak \frac{2}{16} na najprostije elemente rastavlјanjem i kraćenjem 2.

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

Pomnožite 2 i 4 da biste dobili 8.

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

Kvadrat broja \sqrt{3} je 3.

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

Pomnožite 8 i 3 da biste dobili 24.

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

Saberite 24 i 9 da biste dobili 33.

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

Svedite razlomak \frac{33}{18} na najprostije elemente rastavlјanjem i kraćenjem 3.

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

Saberite \frac{1}{8} i \frac{11}{6} da biste dobili \frac{47}{24}.

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

Oduzmite 0 od \frac{47}{24} da biste dobili \frac{47}{24}.

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

Saberite \frac{47}{24} i \frac{1}{24} da biste dobili 2.

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