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

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

Izrēķināt

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

Atrisinājuma darbības

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.

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

Aprēķiniet \frac{1}{2} pakāpē 2 un iegūstiet \frac{1}{4}.

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

Reiziniet 5 un \frac{1}{4}, lai iegūtu \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.

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

Lai kāpinātu izteiksmi \frac{\sqrt{2}}{2}, kāpiniet gan skaitītāju, gan saucēju atbilstoši pakāpei, un pēc tam veiciet dalīšanu.

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

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. Paplašiniet 2^{2}.

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

Tā kā \frac{5}{4} un \frac{\left(\sqrt{2}\right)^{2}}{4} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

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

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

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

Lai kāpinātu izteiksmi \frac{\sqrt{3}}{3}, kāpiniet gan skaitītāju, gan saucēju atbilstoši pakāpei, un pēc tam veiciet dalīšanu.

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

Izsakiet 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} kā vienu daļskaitli.

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

Skaitļa \sqrt{3} kvadrāts ir 3.

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

Reiziniet 4 un 3, lai iegūtu 12.

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

Aprēķiniet 3 pakāpē 2 un iegūstiet 9.

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

Vienādot daļskaitli \frac{12}{9} līdz mazākajam loceklim, izvelkot un saīsinot 3.

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

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. 4 un 3 mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir 12. Reiziniet \frac{5+\left(\sqrt{2}\right)^{2}}{4} reiz \frac{3}{3}. Reiziniet \frac{4}{3} reiz \frac{4}{4}.

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

Tā kā \frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)}{12} un \frac{4\times 4}{12} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

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

Reiziniet 2 un 1,1547005383792515, lai iegūtu 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.

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

Saskaitiet 2,309401076758503 un 1, lai iegūtu 3,309401076758503.

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

Izsakiet \frac{\frac{3\left(5+\left(\sqrt{2}\right)^{2}\right)-4\times 4}{12}}{3,309401076758503} kā vienu daļskaitli.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Saskaitiet 5 un 2, lai iegūtu 7.

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

Reiziniet 3 un 7, lai iegūtu 21.

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

Reiziniet -4 un 4, lai iegūtu -16.

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

Atņemiet 16 no 21, lai iegūtu 5.

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

Reiziniet 12 un 3,309401076758503, lai iegūtu 39,712812921102036.

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

Izvērsiet \frac{5}{39,712812921102036}, reizinot gan skaitītāju, gan saucēju ar 1000000000000000.

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

Vienādot daļskaitli \frac{5000000000000000}{39712812921102036} līdz mazākajam loceklim, izvelkot un saīsinot 4.

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