3tan^{2}30^circ+4tan45^circ+cos30^circoperatorname{ctg}30^circ eching

$$3 \tan ^ { 2 } 30 ^ { \circ } + 4 \tan 45 ^ { \circ } + \cos 30 ^ { \circ } \operatorname { ctg } 30 ^ { \circ }$$

Baholash

$$\frac{13}{2}=6,5$$

Qisqa yechim qadamlari

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

$$3\times \left(\frac{\sqrt{3}}{3}\right)^{2}+4\tan(45)+\cos(30)\cot(30)$$

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

$$3\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}+4\tan(45)+\cos(30)\cot(30)$$

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

$$\frac{3\left(\sqrt{3}\right)^{2}}{3^{2}}+4\tan(45)+\cos(30)\cot(30)$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4\tan(45)+\cos(30)\cot(30)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4\times 1+\cos(30)\cot(30)$$

4 hosil qilish uchun 4 va 1 ni ko'paytirish.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4+\cos(30)\cot(30)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4+\frac{\sqrt{3}}{2}\cot(30)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4+\frac{\sqrt{3}}{2}\sqrt{3}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+4+\frac{\sqrt{3}\sqrt{3}}{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{4\times 3}{3}+\frac{\sqrt{3}\sqrt{3}}{2}$$

\frac{\left(\sqrt{3}\right)^{2}}{3} va \frac{4\times 3}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(\sqrt{3}\right)^{2}+4\times 3}{3}+\frac{\sqrt{3}\sqrt{3}}{2}$$

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

$$\frac{2\left(\sqrt{3}\right)^{2}}{6}+4+\frac{3\sqrt{3}\sqrt{3}}{6}$$

\frac{2\left(\sqrt{3}\right)^{2}}{6} va \frac{3\sqrt{3}\sqrt{3}}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(\sqrt{3}\right)^{2}+3\sqrt{3}\sqrt{3}}{6}+4$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{4\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}$$

\frac{4\times 2}{2} va \frac{\sqrt{3}\sqrt{3}}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{4\times 2+\sqrt{3}\sqrt{3}}{2}$$

4\times 2+\sqrt{3}\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{8+3}{2}$$

8+3 hisob-kitobini qiling.

$$\frac{\left(\sqrt{3}\right)^{2}}{3}+\frac{11}{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{3}{3}+\frac{11}{2}$$

1 ni olish uchun 3 ni 3 ga bo‘ling.

$$1+\frac{11}{2}$$

\frac{13}{2} olish uchun 1 va \frac{11}{2}'ni qo'shing.

$$\frac{13}{2}$$