Whakaoti i te cos60^circ/1+sin60^circ+1/tan30^circ

$$\frac { \cos 60 ^ { \circ } } { 1 + \sin 60 ^ { \circ } } + \frac { 1 } { \tan 30 ^ { \circ } }$$

Aromātai

$$2$$

Ngā Hipanga Rongoā Poto

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

$$\frac{\frac{1}{2}}{1+\sin(60)}+\frac{1}{\tan(30)}$$

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

$$\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}+\frac{1}{\tan(30)}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{2}{2}.

$$\frac{\frac{1}{2}}{\frac{2}{2}+\frac{\sqrt{3}}{2}}+\frac{1}{\tan(30)}$$

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

$$\frac{\frac{1}{2}}{\frac{2+\sqrt{3}}{2}}+\frac{1}{\tan(30)}$$

Whakawehe \frac{1}{2} ki te \frac{2+\sqrt{3}}{2} mā te whakarea \frac{1}{2} ki te tau huripoki o \frac{2+\sqrt{3}}{2}.

$$\frac{2}{2\left(2+\sqrt{3}\right)}+\frac{1}{\tan(30)}$$

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

$$\frac{2}{2\left(2+\sqrt{3}\right)}+\frac{1}{\frac{\sqrt{3}}{3}}$$

Whakawehe 1 ki te \frac{\sqrt{3}}{3} mā te whakarea 1 ki te tau huripoki o \frac{\sqrt{3}}{3}.

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

Whakangāwaritia te tauraro o \frac{3}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Me whakakore te 3 me te 3.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia \sqrt{3} ki te \frac{2\left(2+\sqrt{3}\right)}{2\left(2+\sqrt{3}\right)}.

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

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

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

Mahia ngā whakarea i roto o 2+\sqrt{3}\times 2\left(2+\sqrt{3}\right).

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

Mahia ngā tātaitai i roto o 2+4\sqrt{3}+6.

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

Whakarohaina te 2\left(2+\sqrt{3}\right).

$$\frac{8+4\sqrt{3}}{2\sqrt{3}+4}$$

Whakangāwaritia te tauraro o \frac{8+4\sqrt{3}}{2\sqrt{3}+4} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{3}-4.

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

Whakaarohia te \left(2\sqrt{3}+4\right)\left(2\sqrt{3}-4\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 4 ki te 3, ka 12.

$$\frac{\left(8+4\sqrt{3}\right)\left(2\sqrt{3}-4\right)}{12-4^{2}}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{\left(8+4\sqrt{3}\right)\left(2\sqrt{3}-4\right)}{12-16}$$

Tangohia te 16 i te 12, ka -4.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 8+4\sqrt{3} ki te 2\sqrt{3}-4 ka whakakotahi i ngā kupu rite.

$$\frac{-32+8\left(\sqrt{3}\right)^{2}}{-4}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{-32+8\times 3}{-4}$$

Whakareatia te 8 ki te 3, ka 24.

$$\frac{-32+24}{-4}$$

Tāpirihia te -32 ki te 24, ka -8.

$$\frac{-8}{-4}$$

Whakawehea te -8 ki te -4, kia riro ko 2.

$$2$$