Rešite frac{230^{circ}+cos^{2}45^{circ}-4tan^{2}30^circ}{2sec60^circ*sin30^circ+tan45^circ}

$$\frac { 230 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ } - 4 \tan ^ { 2 } 30 ^ { \circ } } { 2 \sec 60 ^ { \circ } \times \sin 30 ^ { \circ } + \tan 45 ^ { \circ } }$$

Ovrednoti

$$\frac{687500000000000000}{9928203230275509}\approx 69,247172329$$

Koraki rešitve

Evaluate trigonometric functions in the problem

$$\frac{230 + \cos^{2}(45) - 4 \tan^{2}(30)}{2 \cdot 1,1547005383792515 + \tan(45)}$$

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

$$\frac{230+\left(\frac{\sqrt{2}}{2}\right)^{2}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{230+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite 230 s/z \frac{2^{2}}{2^{2}}.

$$\frac{\frac{230\times 2^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

\frac{230\times 2^{2}}{2^{2}} in \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-4\left(\tan(30)\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-4\times \left(\frac{\sqrt{3}}{3}\right)^{2}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Kvadrat vrednosti \sqrt{3} je 3.

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{4\times 3}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Pomnožite 4 in 3, da dobite 12.

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{12}{3^{2}}}{2\times 1,1547005383792515+\tan(45)}$$

Izračunajte potenco 3 števila 2, da dobite 9.

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{12}{9}}{2\times 1,1547005383792515+\tan(45)}$$

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

$$\frac{\frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{4}{3}}{2\times 1,1547005383792515+\tan(45)}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 2^{2} in 3 je 12. Pomnožite \frac{230\times 2^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}} s/z \frac{3}{3}. Pomnožite \frac{4}{3} s/z \frac{4}{4}.

$$\frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)}{12}-\frac{4\times 4}{12}}{2\times 1,1547005383792515+\tan(45)}$$

\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)}{12} in \frac{4\times 4}{12} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2\times 1,1547005383792515+\tan(45)}$$

Pomnožite 2 in 1,1547005383792515, da dobite 2,309401076758503.

$$\frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2,309401076758503+\tan(45)}$$

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

$$\frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{2,309401076758503+1}$$

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

$$\frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3,309401076758503}$$

Izrazite \frac{\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3,309401076758503} kot enojni ulomek.

$$\frac{3\left(230\times 2^{2}+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12\times 3,309401076758503}$$

Izračunajte potenco 2 števila 2, da dobite 4.

$$\frac{3\left(230\times 4+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12\times 3,309401076758503}$$

Pomnožite 230 in 4, da dobite 920.

$$\frac{3\left(920+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12\times 3,309401076758503}$$

Kvadrat vrednosti \sqrt{2} je 2.

$$\frac{3\left(920+2\right)-4\times 4}{12\times 3,309401076758503}$$

Seštejte 920 in 2, da dobite 922.

$$\frac{3\times 922-4\times 4}{12\times 3,309401076758503}$$

Pomnožite 3 in 922, da dobite 2766.

$$\frac{2766-4\times 4}{12\times 3,309401076758503}$$

Pomnožite -4 in 4, da dobite -16.

$$\frac{2766-16}{12\times 3,309401076758503}$$

Odštejte 16 od 2766, da dobite 2750.

$$\frac{2750}{12\times 3,309401076758503}$$

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

$$\frac{2750}{39,712812921102036}$$

Razširite \frac{2750}{39,712812921102036} tako, da pomnožite števec in imenovalec s številom 1000000000000000.

$$\frac{2750000000000000000}{39712812921102036}$$

Zmanjšajte ulomek \frac{2750000000000000000}{39712812921102036} na najmanjši imenovalec tako, da izpeljete in okrajšate 4.

$$\frac{687500000000000000}{9928203230275509}$$