Riješi 1/2tan(15)(sqrt{20}-1)

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

Procijeni

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

Koraci za rješenje

Evaluate trigonometric functions in the problem

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

Pomnožite 2 i 0,2679491924311227 da biste dobili 0,5358983848622454.

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

Proširite \frac{1}{0,5358983848622454} množenjem i brojioca i dijeljenika sa 10000000000000000.

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

Svedite razlomak \frac{10000000000000000}{5358983848622454} na najprostije elemente rastavlјanjem i kraćenjem 2.

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

Faktorirajte 20=2^{2}\times 5. Ponovo napišite kvadratni korijen proizvoda \sqrt{2^{2}\times 5} kao proizvod kvadratnih korijena \sqrt{2^{2}}\sqrt{5}. Izračunajte kvadratni korijen od 2^{2}.

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

Koristite distributivno svojstvo da biste pomnožili \frac{5000000000000000}{2679491924311227} sa 2\sqrt{5}-1.

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

Izrazite \frac{5000000000000000}{2679491924311227}\times 2 kao jedan razlomak.

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

Pomnožite 5000000000000000 i 2 da biste dobili 10000000000000000.

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

Pomnožite \frac{5000000000000000}{2679491924311227} i -1 da biste dobili -\frac{5000000000000000}{2679491924311227}.

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