Whakaoti i te 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

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

Aromātai

$$2$$

Ngā Upane Otinga

Tīkina te uara \sin(30) mai i te ripanga uara pākoki.

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

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

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

Tīkina te uara \cos(45) mai i te ripanga uara pākoki.

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

Kia whakarewa i te \frac{\sqrt{2}}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Me whakarea te \frac{1}{4} ki te \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Tīkina te uara \tan(30) mai i te ripanga uara pākoki.

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

Kia whakarewa i te \frac{\sqrt{3}}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Tuhia te 4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} hei hautanga kotahi.

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

Tīkina te uara \sin(90) mai i te ripanga uara pākoki.

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

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

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

Whakareatia te \frac{1}{2} ki te 1, ka \frac{1}{2}.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4\times 2^{2} me 3^{2} ko 144. Whakareatia \frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}} ki te \frac{9}{9}. Whakareatia \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ki te \frac{16}{16}.

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

Tā te mea he rite te tauraro o \frac{9\left(\sqrt{2}\right)^{2}}{144} me \frac{16\times 4\left(\sqrt{3}\right)^{2}}{144}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4\times 2^{2} me 2 ko 16. Whakareatia \frac{1}{2} ki te \frac{8}{8}.

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

Tā te mea he rite te tauraro o \frac{\left(\sqrt{2}\right)^{2}}{16} me \frac{8}{16}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 3^{2} me 2 ko 18. Whakareatia \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ki te \frac{2}{2}. Whakareatia \frac{1}{2} ki te \frac{9}{9}.

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

Tā te mea he rite te tauraro o \frac{2\times 4\left(\sqrt{3}\right)^{2}}{18} me \frac{9}{18}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tīkina te uara \cos(90) mai i te ripanga uara pākoki.

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

Tātaihia te 0 mā te pū o 2, kia riro ko 0.

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

Whakareatia te 2 ki te 0, ka 0.

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

Tīkina te uara \cos(0) mai i te ripanga uara pākoki.

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

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

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

Whakareatia te \frac{1}{24} ki te 1, ka \frac{1}{24}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Whakareatia te 4 ki te 4, ka 16.

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

Whakahekea te hautanga \frac{2}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Whakareatia te 2 ki te 4, ka 8.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 8 ki te 3, ka 24.

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

Tāpirihia te 24 ki te 9, ka 33.

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

Whakahekea te hautanga \frac{33}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Tāpirihia te \frac{1}{8} ki te \frac{11}{6}, ka \frac{47}{24}.

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

Tangohia te 0 i te \frac{47}{24}, ka \frac{47}{24}.

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

Tāpirihia te \frac{47}{24} ki te \frac{1}{24}, ka 2.

$$2$$