cos(2*30^{circ})=1-tan^230^circ/1+tan^230^circ eching

$$\cos ( 2 \times 30 ^ { \circ } ) = \frac { 1 - \tan ^ { 2 } 30 ^ { \circ } } { 1 + \tan ^ { 2 } 30 ^ { \circ } }$$

Tasdiqlamoq

Yechim qadamlari

60 hosil qilish uchun 2 va 30 ni ko'paytirish.

$$\cos(60)=\frac{1-\left(\tan(30)\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

Trigonometrik qiymatlar jadvaldan \cos(60) qiymatini oling.

$$\frac{1}{2}=\frac{1-\left(\tan(30)\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

Trigonometrik qiymatlar jadvaldan \tan(30) qiymatini oling.

$$\frac{1}{2}=\frac{1-\left(\frac{\sqrt{3}}{3}\right)^{2}}{1+\left(\tan(30)\right)^{2}}$$

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

$$\frac{1}{2}=\frac{1-\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}{1+\left(\tan(30)\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{2}=\frac{1-\frac{3}{3^{2}}}{1+\left(\tan(30)\right)^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{1}{2}=\frac{1-\frac{3}{9}}{1+\left(\tan(30)\right)^{2}}$$

\frac{3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}=\frac{1-\frac{1}{3}}{1+\left(\tan(30)\right)^{2}}$$

\frac{2}{3} olish uchun 1 dan \frac{1}{3} ni ayirish.

$$\frac{1}{2}=\frac{\frac{2}{3}}{1+\left(\tan(30)\right)^{2}}$$

Trigonometrik qiymatlar jadvaldan \tan(30) qiymatini oling.

$$\frac{1}{2}=\frac{\frac{2}{3}}{1+\left(\frac{\sqrt{3}}{3}\right)^{2}}$$

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

$$\frac{1}{2}=\frac{\frac{2}{3}}{1+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{3^{2}}{3^{2}} marotabaga ko'paytirish.

$$\frac{1}{2}=\frac{\frac{2}{3}}{\frac{3^{2}}{3^{2}}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

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

$$\frac{1}{2}=\frac{\frac{2}{3}}{\frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

\frac{2}{3} ni \frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}} ga bo'lish \frac{2}{3} ga k'paytirish \frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}} ga qaytarish.

$$\frac{1}{2}=\frac{2\times 3^{2}}{3\left(3^{2}+\left(\sqrt{3}\right)^{2}\right)}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{1}{2}=\frac{2\times 3}{\left(\sqrt{3}\right)^{2}+3^{2}}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{1}{2}=\frac{6}{\left(\sqrt{3}\right)^{2}+3^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{2}=\frac{6}{3+3^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{1}{2}=\frac{6}{3+9}$$

12 olish uchun 3 va 9'ni qo'shing.

$$\frac{1}{2}=\frac{6}{12}$$

\frac{6}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}=\frac{1}{2}$$

\frac{1}{2} va \frac{1}{2} ni taqqoslang.

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