Rešite 5left(sin(30)right)^2+left(cos(45)right)^2-4left(tan(30)right)^2/2sec(60sin(30))+tan(45)

$$\frac{ 5 { \left( \sin ( 30 ) \right) }^{ 2 } + { \left( \cos ( 45 ) \right) }^{ 2 } -4 { \left( \tan ( 30 ) \right) }^{ 2 } }{ 2 \sec ( 60 \sin ( 30 ) ) + \tan ( 45 ) }$$

Ovrednoti

$$\frac{1250000000000000}{9928203230275509}\approx 0,12590395$$

Koraki rešitve

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.

$$\frac{5\times \left(\frac{1}{2}\right)^{2}+\left(\cos(45)\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Izračunajte potenco \frac{1}{2} števila 2, da dobite \frac{1}{4}.

$$\frac{5\times \frac{1}{4}+\left(\cos(45)\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Pomnožite 5 in \frac{1}{4}, da dobite \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.

$$\frac{\frac{5}{4}+\left(\frac{\sqrt{2}}{2}\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite dobiti potenco vrednosti \frac{\sqrt{2}}{2}, potencirajte števec in imenovalec, nato pa delite.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Razčlenite 2^{2}.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{4}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

\frac{5}{4} in \frac{\left(\sqrt{2}\right)^{2}}{4} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\times \left(\frac{\sqrt{3}}{3}\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite dobiti potenco vrednosti \frac{\sqrt{3}}{3}, potencirajte števec in imenovalec, nato pa delite.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Izrazite 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} kot enojni ulomek.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Kvadrat vrednosti \sqrt{3} je 3.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4\times 3}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Pomnožite 4 in 3, da dobite 12.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{12}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Izračunajte potenco 3 števila 2, da dobite 9.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{12}{9}}{2\times 1,1547005383792515+\tan(45)}$$

Zmanjšajte ulomek \frac{12}{9} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

$$\frac{\frac{5+\left(\sqrt{2}\right)^{2}}{4}-\frac{4}{3}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 4 in 3 je 12. Pomnožite \frac{5+\left(\sqrt{2}\right)^{2}}{4} s/z \frac{3}{3}. Pomnožite \frac{4}{3} s/z \frac{4}{4}.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)}{12}-\frac{4\times 4}{12}}{2\times 1,1547005383792515+\tan(45)}$$

\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)}{12} in \frac{4\times 4}{12} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2\times 1,1547005383792515+\tan(45)}$$

Pomnožite 2 in 1,1547005383792515, da dobite 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.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2,309401076758503+1}$$

Seštejte 2,309401076758503 in 1, da dobite 3,309401076758503.

$$\frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3,309401076758503}$$

Izrazite \frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3,309401076758503} kot enojni ulomek.

$$\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12\times 3,309401076758503}$$

Kvadrat vrednosti \sqrt{2} je 2.

$$\frac{3\left(5+2\right)-4\times 4}{12\times 3,309401076758503}$$

Seštejte 5 in 2, da dobite 7.

$$\frac{3\times 7-4\times 4}{12\times 3,309401076758503}$$

Pomnožite 3 in 7, da dobite 21.

$$\frac{21-4\times 4}{12\times 3,309401076758503}$$

Pomnožite -4 in 4, da dobite -16.

$$\frac{21-16}{12\times 3,309401076758503}$$

Odštejte 16 od 21, da dobite 5.

$$\frac{5}{12\times 3,309401076758503}$$

Pomnožite 12 in 3,309401076758503, da dobite 39,712812921102036.

$$\frac{5}{39,712812921102036}$$

Razširite \frac{5}{39,712812921102036} tako, da pomnožite števec in imenovalec s številom 1000000000000000.

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

Zmanjšajte ulomek \frac{5000000000000000}{39712812921102036} na najmanjši imenovalec tako, da izpeljete in okrajšate 4.

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