Whakaoti i te sin^{2}(60^{circ})-cos^2(30^circ)+tan^2(30^circ)

$$\sin ^ { 2 } ( 60 ^ { \circ } ) - \cos ^ { 2 } ( 30 ^ { \circ } ) + \tan ^ { 2 } ( 30 ^ { \circ } )$$

Aromātai

$$\frac{1}{3}\approx 0.333333333$$

Ngā Upane Otinga

Tīkina te uara \sin(60) mai i te ripanga uara pākoki.

$$\left(\frac{\sqrt{3}}{2}\right)^{2}-\left(\cos(30)\right)^{2}+\left(\tan(30)\right)^{2}$$

Kia whakarewa i te \frac{\sqrt{3}}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\cos(30)\right)^{2}+\left(\tan(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\frac{\sqrt{3}}{2}\right)^{2}+\left(\tan(30)\right)^{2}$$

Kia whakarewa i te \frac{\sqrt{3}}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\tan(30)\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{2^{2}}+\left(\tan(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{4}+\left(\tan(30)\right)^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakarohaina te 2^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}}{4}-\frac{3}{4}+\left(\tan(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}-3}{4}+\left(\tan(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}-3}{4}+\left(\frac{\sqrt{3}}{3}\right)^{2}$$

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.

$$\frac{\left(\sqrt{3}\right)^{2}-3}{4}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4 me 3^{2} ko 36. Whakareatia \frac{\left(\sqrt{3}\right)^{2}-3}{4} ki te \frac{9}{9}. Whakareatia \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} ki te \frac{4}{4}.

$$\frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)}{36}+\frac{4\left(\sqrt{3}\right)^{2}}{36}$$

Tā te mea he rite te tauraro o \frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)}{36} me \frac{4\left(\sqrt{3}\right)^{2}}{36}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)+4\left(\sqrt{3}\right)^{2}}{36}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{3-3}{4}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Tangohia te 3 i te 3, ka 0.

$$\frac{0}{4}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$0+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$0+\frac{3}{3^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$0+\frac{3}{9}$$

Whakahekea te hautanga \frac{3}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$0+\frac{1}{3}$$

Tāpirihia te 0 ki te \frac{1}{3}, ka \frac{1}{3}.

$$\frac{1}{3}$$