frac{5sin^{2}30^{circ}+cos^{2}45^{circ}+4tan^{2}60^{circ}}{2sin^230^circcos60^circ+tan45^circ} eching

$$\frac { 5 \sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ } + 4 \tan ^ { 2 } 60 ^ { \circ } } { 2 \sin ^ { 2 } 30 ^ { \circ } \cos 60 ^ { \circ } + \tan 45 ^ { \circ } }$$

Baholash

$$11$$

Yechim qadamlari

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\frac{5\times \left(\frac{1}{2}\right)^{2}+\left(\cos(45)\right)^{2}+4\left(\tan(60)\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

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

$$\frac{5\times \frac{1}{4}+\left(\cos(45)\right)^{2}+4\left(\tan(60)\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\frac{5}{4} hosil qilish uchun 5 va \frac{1}{4} ni ko'paytirish.

$$\frac{\frac{5}{4}+\left(\cos(45)\right)^{2}+4\left(\tan(60)\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

Trigonometrik qiymatlar jadvaldan \cos(45) qiymatini oling.

$$\frac{\frac{5}{4}+\left(\frac{\sqrt{2}}{2}\right)^{2}+4\left(\tan(60)\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

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

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+4\left(\tan(60)\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

Trigonometrik qiymatlar jadvaldan \tan(60) qiymatini oling.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+4\left(\sqrt{3}\right)^{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\sqrt{3} kvadrati – 3.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+4\times 3}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{\frac{5}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+12}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\frac{53}{4} olish uchun \frac{5}{4} va 12'ni qo'shing.

$$\frac{\frac{53}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\sqrt{2} kvadrati – 2.

$$\frac{\frac{53}{4}+\frac{2}{2^{2}}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

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

$$\frac{\frac{53}{4}+\frac{2}{4}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{53}{4}+\frac{1}{2}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

\frac{55}{4} olish uchun \frac{53}{4} va \frac{1}{2}'ni qo'shing.

$$\frac{\frac{55}{4}}{2\left(\sin(30)\right)^{2}\cos(60)+\tan(45)}$$

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\frac{\frac{55}{4}}{2\times \left(\frac{1}{2}\right)^{2}\cos(60)+\tan(45)}$$

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

$$\frac{\frac{55}{4}}{2\times \frac{1}{4}\cos(60)+\tan(45)}$$

\frac{1}{2} hosil qilish uchun 2 va \frac{1}{4} ni ko'paytirish.

$$\frac{\frac{55}{4}}{\frac{1}{2}\cos(60)+\tan(45)}$$

Trigonometrik qiymatlar jadvaldan \cos(60) qiymatini oling.

$$\frac{\frac{55}{4}}{\frac{1}{2}\times \frac{1}{2}+\tan(45)}$$

\frac{1}{4} hosil qilish uchun \frac{1}{2} va \frac{1}{2} ni ko'paytirish.

$$\frac{\frac{55}{4}}{\frac{1}{4}+\tan(45)}$$

Trigonometrik qiymatlar jadvaldan \tan(45) qiymatini oling.

$$\frac{\frac{55}{4}}{\frac{1}{4}+1}$$

\frac{5}{4} olish uchun \frac{1}{4} va 1'ni qo'shing.

$$\frac{\frac{55}{4}}{\frac{5}{4}}$$

\frac{55}{4} ni \frac{5}{4} ga bo'lish \frac{55}{4} ga k'paytirish \frac{5}{4} ga qaytarish.

$$\frac{55}{4}\times \frac{4}{5}$$

11 hosil qilish uchun \frac{55}{4} va \frac{4}{5} ni ko'paytirish.

$$11$$