left(sin(30)right)^2left(cos(45)right)^2+4left(tan(30)right)^2+1/2left(sin(90)right)^2-2{left(cos(90)right)}^2+1/24{left(cos(0)right)}^2 eching

$${ \left( \sin ( 30 ) \right) }^{ 2 } { \left( \cos ( 45 ) \right) }^{ 2 } +4 { \left( \tan ( 30 ) \right) }^{ 2 } + \frac{ 1 }{ 2 } { \left( \sin ( 90 ) \right) }^{ 2 } -2 { \left( \cos ( 90 ) \right) }^{ 2 } + \frac{ 1 }{ 24 } { \left( \cos ( 0 ) \right) }^{ 2 }$$

Baholash

$$2$$

Yechim qadamlari

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\left(\frac{1}{2}\right)^{2}\left(\cos(45)\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

2 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{1}{4}\left(\cos(45)\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \cos(45) qiymatini oling.

$$\frac{1}{4}\times \left(\frac{\sqrt{2}}{2}\right)^{2}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{1}{4}\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{4} ni \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} ga ko‘paytiring.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\left(\tan(30)\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \tan(30) qiymatini oling.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\times \left(\frac{\sqrt{3}}{3}\right)^{2}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+4\times \frac{\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\left(\sin(90)\right)^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \sin(90) qiymatini oling.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\times 1^{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}\times 1-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

\frac{1}{2} hosil qilish uchun \frac{1}{2} va 1 ni ko'paytirish.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4\times 2^{2} va 3^{2} ning eng kichik umumiy karralisi 144. \frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}} ni \frac{9}{9} marotabaga ko'paytirish. \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ni \frac{16}{16} marotabaga ko'paytirish.

$$\frac{9\left(\sqrt{2}\right)^{2}}{144}+\frac{16\times 4\left(\sqrt{3}\right)^{2}}{144}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

\frac{9\left(\sqrt{2}\right)^{2}}{144} va \frac{16\times 4\left(\sqrt{3}\right)^{2}}{144} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{9\left(\sqrt{2}\right)^{2}+16\times 4\left(\sqrt{3}\right)^{2}}{144}+\frac{1}{2}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4\times 2^{2} va 2 ning eng kichik umumiy karralisi 16. \frac{1}{2} ni \frac{8}{8} marotabaga ko'paytirish.

$$\frac{\left(\sqrt{2}\right)^{2}}{16}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}+\frac{8}{16}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

\frac{\left(\sqrt{2}\right)^{2}}{16} va \frac{8}{16} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(\sqrt{2}\right)^{2}+8}{16}+\frac{4\left(\sqrt{3}\right)^{2}}{3^{2}}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3^{2} va 2 ning eng kichik umumiy karralisi 18. \frac{4\left(\sqrt{3}\right)^{2}}{3^{2}} ni \frac{2}{2} marotabaga ko'paytirish. \frac{1}{2} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}}{18}+\frac{9}{18}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

\frac{2\times 4\left(\sqrt{3}\right)^{2}}{18} va \frac{9}{18} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\left(\cos(90)\right)^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \cos(90) qiymatini oling.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\times 0^{2}+\frac{1}{24}\left(\cos(0)\right)^{2}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-2\times 0+\frac{1}{24}\left(\cos(0)\right)^{2}$$

0 hosil qilish uchun 2 va 0 ni ko'paytirish.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\left(\cos(0)\right)^{2}$$

Trigonometrik qiymatlar jadvaldan \cos(0) qiymatini oling.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\times 1^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}\times 1$$

\frac{1}{24} hosil qilish uchun \frac{1}{24} va 1 ni ko'paytirish.

$$\frac{\left(\sqrt{2}\right)^{2}}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

\sqrt{2} kvadrati – 2.

$$\frac{2}{4\times 2^{2}}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

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

$$\frac{2}{4\times 4}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

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

$$\frac{2}{16}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

\frac{2}{16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{8}+\frac{2\times 4\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$\frac{1}{8}+\frac{8\left(\sqrt{3}\right)^{2}+9}{18}-0+\frac{1}{24}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{8}+\frac{8\times 3+9}{18}-0+\frac{1}{24}$$

24 hosil qilish uchun 8 va 3 ni ko'paytirish.

$$\frac{1}{8}+\frac{24+9}{18}-0+\frac{1}{24}$$

33 olish uchun 24 va 9'ni qo'shing.

$$\frac{1}{8}+\frac{33}{18}-0+\frac{1}{24}$$

\frac{33}{18} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{8}+\frac{11}{6}-0+\frac{1}{24}$$

\frac{47}{24} olish uchun \frac{1}{8} va \frac{11}{6}'ni qo'shing.

$$\frac{47}{24}-0+\frac{1}{24}$$

\frac{47}{24} olish uchun \frac{47}{24} dan 0 ni ayirish.

$$\frac{47}{24}+\frac{1}{24}$$

2 olish uchun \frac{47}{24} va \frac{1}{24}'ni qo'shing.

$$2$$