Rešite 1/2tan(15)(sqrt{20}-1)

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

Ovrednoti

$$\frac{10000000000000000\sqrt{5}-5000000000000000}{2679491924311227}\approx 6,479093897$$

Koraki rešitve

Evaluate trigonometric functions in the problem

$$\frac{1}{2 \cdot 0,2679491924311227} {(\sqrt{20} - 1)}$$

Pomnožite 2 in 0,2679491924311227, da dobite 0,5358983848622454.

$$\frac{1}{0,5358983848622454}\left(\sqrt{20}-1\right)$$

Razširite \frac{1}{0,5358983848622454} tako, da pomnožite števec in imenovalec s številom 10000000000000000.

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

Zmanjšajte ulomek \frac{10000000000000000}{5358983848622454} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

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

Faktorizirajte 20=2^{2}\times 5. Znova napišite kvadratni koren izdelka \sqrt{2^{2}\times 5} kot produkt kvadratnih korenov \sqrt{2^{2}}\sqrt{5}. Uporabite kvadratni koren števila 2^{2}.

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

Uporabite distributivnost, da pomnožite \frac{5000000000000000}{2679491924311227} s/z 2\sqrt{5}-1.

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

Izrazite \frac{5000000000000000}{2679491924311227}\times 2 kot enojni ulomek.

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

Pomnožite 5000000000000000 in 2, da dobite 10000000000000000.

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

Pomnožite \frac{5000000000000000}{2679491924311227} in -1, da dobite -\frac{5000000000000000}{2679491924311227}.

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