sin(150-120)=sin(150)*cos(120)-sin(120)*cos(150) eching

$$\sin ( 150-120 ) = \sin ( 150 ) \times \cos ( 120 ) - \sin ( 120 ) \times \cos ( 150 )$$

Tasdiqlamoq

Yechim qadamlari

30 olish uchun 150 dan 120 ni ayirish.

$$\sin(30)=\sin(150)\cos(120)-\sin(120)\cos(150)$$

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\frac{1}{2}=\sin(150)\cos(120)-\sin(120)\cos(150)$$

Natija olish uchun \sin(x)\cos(y)=\frac{1}{2}\left(\sin(x-y)+\sin(x+y)\right) formulasidan foydalaning.

$$\frac{1}{2}=\frac{1}{2}\left(\sin(150-120)+\sin(150+120)\right)-\sin(120)\cos(150)$$

150 dan 120 ni ayirish. 120 ni 150 ga qo'shish.

$$\frac{1}{2}=\frac{1}{2}\left(\sin(30)+\sin(270)\right)-\sin(120)\cos(150)$$

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\frac{1}{2}=\frac{1}{2}\left(\frac{1}{2}+\sin(270)\right)-\sin(120)\cos(150)$$

Trigonometrik qiymatlar jadvaldan \sin(270) qiymatini oling.

$$\frac{1}{2}=\frac{1}{2}\left(\frac{1}{2}-1\right)-\sin(120)\cos(150)$$

Hisoblarni amalga oshiring.

$$\frac{1}{2}=-\frac{1}{4}-\sin(120)\cos(150)$$

Natija olish uchun \sin(x)\cos(y)=\frac{1}{2}\left(\sin(x-y)+\sin(x+y)\right) formulasidan foydalaning.

$$\frac{1}{2}=-\frac{1}{4}-\frac{1}{2}\left(\sin(120-150)+\sin(120+150)\right)$$

120 dan 150 ni ayirish. 150 ni 120 ga qo'shish.

$$\frac{1}{2}=-\frac{1}{4}-\frac{1}{2}\left(\sin(-30)+\sin(270)\right)$$

\sin(-x)=-\sin(x) xususiyatidan foydalaning.

$$\frac{1}{2}=-\frac{1}{4}-\frac{1}{2}\left(-\sin(30)+\sin(270)\right)$$

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$\frac{1}{2}=-\frac{1}{4}-\frac{1}{2}\left(-\frac{1}{2}+\sin(270)\right)$$

Trigonometrik qiymatlar jadvaldan \sin(270) qiymatini oling.

$$\frac{1}{2}=-\frac{1}{4}-\frac{1}{2}\left(-\frac{1}{2}-1\right)$$

Hisoblarni amalga oshiring.

$$\frac{1}{2}=-\frac{1}{4}-\left(-\frac{3}{4}\right)$$

-\frac{3}{4} ning teskarisi \frac{3}{4} ga teng.

$$\frac{1}{2}=-\frac{1}{4}+\frac{3}{4}$$

\frac{1}{2} olish uchun -\frac{1}{4} va \frac{3}{4}'ni qo'shing.

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

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

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