4(sin150^{circ}cos135^circ+cos240^circsin135^circ)sin45^circ eching

$$4 ( \sin 150 ^ { \circ } \cos 135 ^ { \circ } + \cos 240 ^ { \circ } \sin 135 ^ { \circ } ) \sin 45 ^ { \circ }$$

Baholash

$$-2$$

Yechim qadamlari

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

$$4\left(\frac{1}{2}\left(\sin(150-135)+\sin(150+135)\right)+\cos(240)\sin(135)\right)\sin(45)$$

150 dan 135 ni ayirish. 135 ni 150 ga qo'shish.

$$4\left(\frac{1}{2}\left(\sin(15)+\sin(285)\right)+\cos(240)\sin(135)\right)\sin(45)$$

Hisoblarni amalga oshiring.

$$4\left(-\frac{1}{4}\sqrt{2}+\cos(240)\sin(135)\right)\sin(45)$$

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

$$4\left(-\frac{1}{4}\sqrt{2}+\frac{1}{2}\left(\sin(135-240)+\sin(135+240)\right)\right)\sin(45)$$

135 dan 240 ni ayirish. 240 ni 135 ga qo'shish.

$$4\left(-\frac{1}{4}\sqrt{2}+\frac{1}{2}\left(\sin(-105)+\sin(375)\right)\right)\sin(45)$$

Hisoblarni amalga oshiring.

$$4\left(-\frac{1}{4}\sqrt{2}-\frac{1}{4}\sqrt{2}\right)\sin(45)$$

-\frac{1}{2}\sqrt{2} ni olish uchun -\frac{1}{4}\sqrt{2} va -\frac{1}{4}\sqrt{2} ni birlashtirish.

$$4\left(-\frac{1}{2}\right)\sqrt{2}\sin(45)$$

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

$$-2\sqrt{2}\sin(45)$$

Trigonometrik qiymatlar jadvaldan \sin(45) qiymatini oling.

$$-2\sqrt{2}\times \frac{\sqrt{2}}{2}$$

2 va 2 ni qisqartiring.

$$-\sqrt{2}\sqrt{2}$$

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

$$-2$$