Whakaoti i te 2tan^{2}45^{circ}+cos^230^circ-sin^260^circ

$$2 \tan ^ { 2 } 45 ^ { \circ } + \cos ^ { 2 } 30 ^ { \circ } - \sin ^ { 2 } 60 ^ { \circ }$$

Aromātai

$$2$$

Ngā Upane Otinga

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

$$2\times 1^{2}+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

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

$$2\times 1+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

Whakareatia te 2 ki te 1, ka 2.

$$2+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

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

$$2+\left(\frac{\sqrt{3}}{2}\right)^{2}-\left(\sin(60)\right)^{2}$$

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.

$$2+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\sin(60)\right)^{2}$$

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

$$\frac{2\times 2^{2}}{2^{2}}+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\sin(60)\right)^{2}$$

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

$$\frac{2\times 2^{2}+\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\sin(60)\right)^{2}$$

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

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

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.

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

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

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

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

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

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

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

Tātaihia te 2 mā te pū o 3, kia riro ko 8.

$$\frac{8+\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{4}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{8+3}{2^{2}}-\frac{3}{4}$$

Tāpirihia te 8 ki te 3, ka 11.

$$\frac{11}{2^{2}}-\frac{3}{4}$$

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

$$\frac{11}{4}-\frac{3}{4}$$

Tangohia te \frac{3}{4} i te \frac{11}{4}, ka 2.

$$2$$