6tan^230^circ-sqrt{3}sin60^circ-2sin45^circ eching

$$6 \tan ^ { 2 } 30 ^ { \circ } - \sqrt { 3 } \sin 60 ^ { \circ } - 2 \sin 45 ^ { \circ }$$

Baholash

$$\frac{1}{2}-\sqrt{2}\approx -0,914213562$$

Yechim qadamlari

Get the value of \tan(30) from trigonometric values table.

$$6\times \left(\frac{\sqrt{3}}{3}\right)^{2}-\sqrt{3}\sin(60)-2\sin(45)$$

\frac{\sqrt{3}}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$6\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\sin(60)-2\sin(45)$$

6\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} ni yagona kasrga aylantiring.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\sin(60)-2\sin(45)$$

Get the value of \sin(60) from trigonometric values table.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\sqrt{3}\times \frac{\sqrt{3}}{2}-2\sin(45)$$

\sqrt{3}\times \frac{\sqrt{3}}{2} ni yagona kasrga aylantiring.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\frac{\sqrt{3}\sqrt{3}}{2}-2\sin(45)$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{6\left(\sqrt{3}\right)^{2}}{3^{2}}-\frac{3}{2}-2\sin(45)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3^{2} va 2 ning eng kichik umumiy karralisi 18. \frac{6\left(\sqrt{3}\right)^{2}}{3^{2}} ni \frac{2}{2} marotabaga ko'paytirish. \frac{3}{2} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}}{18}-\frac{3\times 9}{18}-2\sin(45)$$

\frac{2\times 6\left(\sqrt{3}\right)^{2}}{18} va \frac{3\times 9}{18} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-2\sin(45)$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-2\times \frac{\sqrt{2}}{2}$$

2 va 2 ni qisqartiring.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\sqrt{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \sqrt{2} ni \frac{18}{18} marotabaga ko'paytirish.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\frac{18\sqrt{2}}{18}$$

\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9}{18} va \frac{18\sqrt{2}}{18} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\times 6\left(\sqrt{3}\right)^{2}-3\times 9-18\sqrt{2}}{18}$$

Ko‘paytirishlarni bajaring.

$$\frac{12\left(\sqrt{3}\right)^{2}-3\times 9}{18}-\sqrt{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{12\times 3-3\times 9}{18}-\sqrt{2}$$

36 hosil qilish uchun 12 va 3 ni ko'paytirish.

$$\frac{36-3\times 9}{18}-\sqrt{2}$$

-27 hosil qilish uchun -3 va 9 ni ko'paytirish.

$$\frac{36-27}{18}-\sqrt{2}$$

9 olish uchun 36 dan 27 ni ayirish.

$$\frac{9}{18}-\sqrt{2}$$

\frac{9}{18} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}-\sqrt{2}$$