sin^{2}(60^{circ})-cos^2(30^circ)+tan^2(30^circ) eching

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

Baholash

$$\frac{1}{3}\approx 0,333333333$$

Yechim qadamlari

Trigonometrik qiymatlar jadvaldan \sin(60) qiymatini oling.

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

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

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

Trigonometrik qiymatlar jadvaldan \cos(30) qiymatini oling.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

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

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

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

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

Trigonometrik qiymatlar jadvaldan \tan(30) qiymatini oling.

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

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

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 va 3^{2} ning eng kichik umumiy karralisi 36. \frac{\left(\sqrt{3}\right)^{2}-3}{4} ni \frac{9}{9} marotabaga ko'paytirish. \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} ni \frac{4}{4} marotabaga ko'paytirish.

$$\frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)}{36}+\frac{4\left(\sqrt{3}\right)^{2}}{36}$$

\frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)}{36} va \frac{4\left(\sqrt{3}\right)^{2}}{36} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{9\left(\left(\sqrt{3}\right)^{2}-3\right)+4\left(\sqrt{3}\right)^{2}}{36}$$

\sqrt{3} kvadrati – 3.

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

0 olish uchun 3 dan 3 ni ayirish.

$$\frac{0}{4}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$0+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

\sqrt{3} kvadrati – 3.

$$0+\frac{3}{3^{2}}$$

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

$$0+\frac{3}{9}$$

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

$$0+\frac{1}{3}$$

\frac{1}{3} olish uchun 0 va \frac{1}{3}'ni qo'shing.

$$\frac{1}{3}$$