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

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

Evaluate

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

Solution Steps

Evaluate trigonometric functions in the problem

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

Multiply 2 and 0.2679491924311227 to get 0.5358983848622454.

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

Expand \frac{1}{0.5358983848622454} by multiplying both numerator and the denominator by 10000000000000000.

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

Reduce the fraction \frac{10000000000000000}{5358983848622454} to lowest terms by extracting and canceling out 2.

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

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Use the distributive property to multiply \frac{5000000000000000}{2679491924311227} by 2\sqrt{5}-1.

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

Express \frac{5000000000000000}{2679491924311227}\times 2 as a single fraction.

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

Multiply 5000000000000000 and 2 to get 10000000000000000.

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

Multiply \frac{5000000000000000}{2679491924311227} and -1 to get -\frac{5000000000000000}{2679491924311227}.

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