Lutasin ang 1/2tan(15)(sqrt{20}-1)

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

I-evaluate

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

Mga Hakbang ng Solution

Evaluate trigonometric functions in the problem

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

I-multiply ang 2 at 0.2679491924311227 para makuha ang 0.5358983848622454.

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

I-expand ang \frac{1}{0.5358983848622454} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 10000000000000000.

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

Bawasan ang fraction \frac{10000000000000000}{5358983848622454} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 2.

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

I-factor out ang 20=2^{2}\times 5. I-rewrite ang square root ng product na \sqrt{2^{2}\times 5} bilang product ng mga square root na \sqrt{2^{2}}\sqrt{5}. Kunin ang square root ng 2^{2}.

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

Gamitin ang distributive property para i-multiply ang \frac{5000000000000000}{2679491924311227} gamit ang 2\sqrt{5}-1.

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

Ipakita ang \frac{5000000000000000}{2679491924311227}\times 2 bilang isang single fraction.

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

I-multiply ang 5000000000000000 at 2 para makuha ang 10000000000000000.

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

I-multiply ang \frac{5000000000000000}{2679491924311227} at -1 para makuha ang -\frac{5000000000000000}{2679491924311227}.

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