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

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

Baholash

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

Yechim qadamlari

Evaluate trigonometric functions in the problem

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

0,5358983848622454 hosil qilish uchun 2 va 0,2679491924311227 ni ko'paytirish.

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

\frac{1}{0,5358983848622454} kasrini uning surat va maxrajini 10000000000000000 ga ko‘paytirish bilan kengaytiring.

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

\frac{10000000000000000}{5358983848622454} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Faktor: 20=2^{2}\times 5. \sqrt{2^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

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

\frac{5000000000000000}{2679491924311227} ga 2\sqrt{5}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{5000000000000000}{2679491924311227}\times 2 ni yagona kasrga aylantiring.

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

10000000000000000 hosil qilish uchun 5000000000000000 va 2 ni ko'paytirish.

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

-\frac{5000000000000000}{2679491924311227} hosil qilish uchun \frac{5000000000000000}{2679491924311227} va -1 ni ko'paytirish.

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