Whakaoti i te 1/2tan(15)(sqrt{20}-1)

$$\frac{ 1 }{ 2 \tan ( 15 ) } ( \sqrt{ 20 } -1)$$

Aromātai

$$\frac{10000000000000000\sqrt{5}-5000000000000000}{2679491924311227}\approx 6.479093897$$

Ngā Upane Otinga

Evaluate trigonometric functions in the problem

$$\frac{1}{2 \cdot 0.2679491924311227} {(\sqrt{20} - 1)}$$

Whakareatia te 2 ki te 0.2679491924311227, ka 0.5358983848622454.

$$\frac{1}{0.5358983848622454}\left(\sqrt{20}-1\right)$$

Whakarohaina te \frac{1}{0.5358983848622454} mā te whakarea i te taurunga me te tauraro ki te 10000000000000000.

$$\frac{10000000000000000}{5358983848622454}\left(\sqrt{20}-1\right)$$

Whakahekea te hautanga \frac{10000000000000000}{5358983848622454} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5000000000000000}{2679491924311227}\left(\sqrt{20}-1\right)$$

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{5000000000000000}{2679491924311227}\left(2\sqrt{5}-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{5000000000000000}{2679491924311227} ki te 2\sqrt{5}-1.

$$\frac{5000000000000000}{2679491924311227}\times 2\sqrt{5}+\frac{5000000000000000}{2679491924311227}\left(-1\right)$$

Tuhia te \frac{5000000000000000}{2679491924311227}\times 2 hei hautanga kotahi.

$$\frac{5000000000000000\times 2}{2679491924311227}\sqrt{5}+\frac{5000000000000000}{2679491924311227}\left(-1\right)$$

Whakareatia te 5000000000000000 ki te 2, ka 10000000000000000.

$$\frac{10000000000000000}{2679491924311227}\sqrt{5}+\frac{5000000000000000}{2679491924311227}\left(-1\right)$$

Whakareatia te \frac{5000000000000000}{2679491924311227} ki te -1, ka -\frac{5000000000000000}{2679491924311227}.

$$\frac{10000000000000000}{2679491924311227}\sqrt{5}-\frac{5000000000000000}{2679491924311227}$$