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

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

I-evaluate

$$\frac{10000000000000000\sqrt{5}}{2679491924311227}-1\approx 7.345119301$$

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.

$$\frac{1}{0.5358983848622454}\sqrt{20}-1$$

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

$$\frac{10000000000000000}{5358983848622454}\sqrt{20}-1$$

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

$$\frac{5000000000000000}{2679491924311227}\sqrt{20}-1$$

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}.

$$\frac{5000000000000000}{2679491924311227}\times 2\sqrt{5}-1$$

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

$$\frac{5000000000000000\times 2}{2679491924311227}\sqrt{5}-1$$

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

$$\frac{10000000000000000}{2679491924311227}\sqrt{5}-1$$

I-factor

$$\frac{10000000000000000 \sqrt{5}}{2679491924311227} - 1 = 7.345119301$$