Whakaoti i te 6tan^230^circ-sqrt{3}sin60^circ-2sin45^circ

$$6 \tan ^ { 2 } 30 ^ { \circ } - \sqrt { 3 } \sin 60 ^ { \circ } - 2 \sin 45 ^ { \circ }$$

Aromātai

$$\frac{1}{2}-\sqrt{2}\approx -0.914213562$$

Ngā Upane Otinga

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

$$6\times \left(\frac{\sqrt{3}}{3}\right)^{2}-\sqrt{3}\sin(60)-2\sin(45)$$

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.

$$6\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\sin(60)-2\sin(45)$$

Tuhia te 6\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} hei hautanga kotahi.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\sin(60)-2\sin(45)$$

Get the value of \sin(60) from trigonometric values table.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\times \frac{\sqrt{3}}{2}-2\sin(45)$$

Tuhia te \sqrt{3}\times \frac{\sqrt{3}}{2} hei hautanga kotahi.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\frac{\sqrt{3}\sqrt{3}}{2}-2\sin(45)$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\frac{3}{2}-2\sin(45)$$

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{6\left(\sqrt{3}\right)^{2}}{3^{2}} ki te \frac{2}{2}. Whakareatia \frac{3}{2} ki te \frac{9}{9}.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}}{18}-\frac{3\times 9}{18}-2\sin(45)$$

Tā te mea he rite te tauraro o \frac{2\times 6\left(\sqrt{3}\right)^{2}}{18} me \frac{3\times 9}{18}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-2\sin(45)$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-2\times \frac{\sqrt{2}}{2}$$

Me whakakore te 2 me te 2.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\sqrt{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia \sqrt{2} ki te \frac{18}{18}.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\frac{18\sqrt{2}}{18}$$

Tā te mea he rite te tauraro o \frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18} me \frac{18\sqrt{2}}{18}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9-18\sqrt{2}}{18}$$

Mahia ngā whakarea.

$$\frac{12\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\sqrt{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12\times 3-3\times 9}{18}-\sqrt{2}$$

Whakareatia te 12 ki te 3, ka 36.

$$\frac{36-3\times 9}{18}-\sqrt{2}$$

Whakareatia te -3 ki te 9, ka -27.

$$\frac{36-27}{18}-\sqrt{2}$$

Tangohia te 27 i te 36, ka 9.

$$\frac{9}{18}-\sqrt{2}$$

Whakahekea te hautanga \frac{9}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$\frac{1}{2}-\sqrt{2}$$