Whakaoti i te 3tan^{2}30^circ+4tan45^circ+cos30^circoperatorname{ctg}30^circ

$$3 \tan ^ { 2 } 30 ^ { \circ } + 4 \tan 45 ^ { \circ } + \cos 30 ^ { \circ } \operatorname { ctg } 30 ^ { \circ }$$

Aromātai

$$\frac{13}{2}=6.5$$

Ngā Hipanga Rongoā Poto

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

$$3\times \left(\frac{\sqrt{3}}{3}\right)^{2}+4\tan(45)+\cos(30)\cot(30)$$

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.

$$3\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}+4\tan(45)+\cos(30)\cot(30)$$

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

$$\frac{3\left(\sqrt{3}\right)^{2}}{3^{2}}+4\tan(45)+\cos(30)\cot(30)$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4\tan(45)+\cos(30)\cot(30)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4\times 1+\cos(30)\cot(30)$$

Whakareatia te 4 ki te 1, ka 4.

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

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

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

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

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

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

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4 ki te \frac{3}{3}.

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

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

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 3 me 2 ko 6. Whakareatia \frac{\left(\sqrt{3}\right)^{2}}{3} ki te \frac{2}{2}. Whakareatia \frac{\sqrt{3}\sqrt{3}}{2} ki te \frac{3}{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}}{6}+4+\frac{3\sqrt{3}\sqrt{3}}{6}$$

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

$$\frac{2\left(\sqrt{3}\right)^{2}+3\sqrt{3}\sqrt{3}}{6}+4$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4 ki te \frac{2}{2}.

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

Tā te mea he rite te tauraro o \frac{4\times 2}{2} me \frac{\sqrt{3}\sqrt{3}}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Mahia ngā whakarea i roto o 4\times 2+\sqrt{3}\sqrt{3}.

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

Mahia ngā tātaitai i roto o 8+3.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{11}{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{3}{3}+\frac{11}{2}$$

Whakawehea te 3 ki te 3, kia riro ko 1.

$$1+\frac{11}{2}$$

Tāpirihia te 1 ki te \frac{11}{2}, ka \frac{13}{2}.

$$\frac{13}{2}$$