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

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

Calcular

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

Pasos da solución

Evaluate trigonometric functions in the problem

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

Multiplica 2 e 0.2679491924311227 para obter 0.5358983848622454.

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

Expande \frac{1}{0.5358983848622454} multiplicando o numerador e o denominador por 10000000000000000.

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

Reduce a fracción \frac{10000000000000000}{5358983848622454} a termos máis baixos extraendo e cancelando 2.

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

Factoriza 20=2^{2}\times 5. Reescribe a raíz cadrada do produto \sqrt{2^{2}\times 5} como o produto de raíces cadradas \sqrt{2^{2}}\sqrt{5}. Obtén a raíz cadrada de 2^{2}.

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

Usa a propiedade distributiva para multiplicar \frac{5000000000000000}{2679491924311227} por 2\sqrt{5}-1.

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

Expresa \frac{5000000000000000}{2679491924311227}\times 2 como unha única fracción.

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

Multiplica 5000000000000000 e 2 para obter 10000000000000000.

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

Multiplica \frac{5000000000000000}{2679491924311227} e -1 para obter -\frac{5000000000000000}{2679491924311227}.

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