2tan^{2}45^{circ}+cos^230^circ-sin^260^circ eching

$$2 \tan ^ { 2 } 45 ^ { \circ } + \cos ^ { 2 } 30 ^ { \circ } - \sin ^ { 2 } 60 ^ { \circ }$$

Baholash

$$2$$

Yechim qadamlari

Trigonometrik qiymatlar jadvaldan \tan(45) qiymatini oling.

$$2\times 1^{2}+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$2\times 1+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$2+\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \cos(30) qiymatini oling.

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

\frac{\sqrt{3}}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

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

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

Trigonometrik qiymatlar jadvaldan \sin(60) qiymatini oling.

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

\frac{\sqrt{3}}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

\sqrt{3} kvadrati – 3.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2^{2} ni kengaytirish.

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

\frac{2\times 2^{2}+\left(\sqrt{3}\right)^{2}}{4} va \frac{3}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

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

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$\frac{8+\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{4}$$

\sqrt{3} kvadrati – 3.

$$\frac{8+3}{2^{2}}-\frac{3}{4}$$

11 olish uchun 8 va 3'ni qo'shing.

$$\frac{11}{2^{2}}-\frac{3}{4}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{11}{4}-\frac{3}{4}$$

2 olish uchun \frac{11}{4} dan \frac{3}{4} ni ayirish.

$$2$$