Lahenda 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

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

Arvuta

$$2$$

Lahenduse etapid

Leidke \sin(30) väärtus trigonomeetriliste väärtuste tabelist.

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

Arvutage 2 aste \frac{1}{2} ja leidke \frac{1}{4}.

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

Leidke \cos(45) väärtus trigonomeetriliste väärtuste tabelist.

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

Avaldise \frac{\sqrt{2}}{2} astendamiseks astendage nii lugeja kui ka nimetaja ning seejärel tehke jagamistehe.

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

Korrutage omavahel \frac{1}{4} ja \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Leidke \tan(30) väärtus trigonomeetriliste väärtuste tabelist.

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

Avaldise \frac{\sqrt{3}}{3} astendamiseks astendage nii lugeja kui ka nimetaja ning seejärel tehke jagamistehe.

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

Avaldage 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} ühe murdarvuna.

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

Leidke \sin(90) väärtus trigonomeetriliste väärtuste tabelist.

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

Arvutage 2 aste 1 ja leidke 1.

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

Korrutage \frac{1}{2} ja 1, et leida \frac{1}{2}.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. 4\times 2^{2} ja 3^{2} vähim ühiskordne on 144. Korrutage omavahel \frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}} ja \frac{9}{9}. Korrutage omavahel \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ja \frac{16}{16}.

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

Kuna murdudel \frac{9\left(\sqrt{2}\right)^{2}}{144} ja \frac{16\times 4\left(\sqrt{3}\right)^{2}}{144} on sama nimetaja, liitke nende lugejad.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. 4\times 2^{2} ja 2 vähim ühiskordne on 16. Korrutage omavahel \frac{1}{2} ja \frac{8}{8}.

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

Kuna murdudel \frac{\left(\sqrt{2}\right)^{2}}{16} ja \frac{8}{16} on sama nimetaja, liitke nende lugejad.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. 3^{2} ja 2 vähim ühiskordne on 18. Korrutage omavahel \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ja \frac{2}{2}. Korrutage omavahel \frac{1}{2} ja \frac{9}{9}.

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

Kuna murdudel \frac{2\times 4\left(\sqrt{3}\right)^{2}}{18} ja \frac{9}{18} on sama nimetaja, liitke nende lugejad.

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

Leidke \cos(90) väärtus trigonomeetriliste väärtuste tabelist.

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

Arvutage 2 aste 0 ja leidke 0.

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

Korrutage 2 ja 0, et leida 0.

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

Leidke \cos(0) väärtus trigonomeetriliste väärtuste tabelist.

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

Arvutage 2 aste 1 ja leidke 1.

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

Korrutage \frac{1}{24} ja 1, et leida \frac{1}{24}.

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

\sqrt{2} ruut on 2.

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

Arvutage 2 aste 2 ja leidke 4.

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

Korrutage 4 ja 4, et leida 16.

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

Taandage murd \frac{2}{16} vähimale ühiskordsele, eraldades ja taandades arvu 2.

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

Korrutage 2 ja 4, et leida 8.

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

\sqrt{3} ruut on 3.

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

Korrutage 8 ja 3, et leida 24.

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

Liitke 24 ja 9, et leida 33.

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

Taandage murd \frac{33}{18} vähimale ühiskordsele, eraldades ja taandades arvu 3.

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

Liitke \frac{1}{8} ja \frac{11}{6}, et leida \frac{47}{24}.

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

Lahutage 0 väärtusest \frac{47}{24}, et leida \frac{47}{24}.

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

Liitke \frac{47}{24} ja \frac{1}{24}, et leida 2.

$$2$$