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

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

Luacháil

$$-2$$

Céimeanna Réitigh

Bain úsáid as \sin(x)\cos(y)=\frac{1}{2}\left(\sin(x-y)+\sin(x+y)\right) chun an toradh a fháil.

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

Dealaigh 135 ó 150. Suimigh 135 le 150?

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

Déan áirimh.

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

Bain úsáid as \sin(x)\cos(y)=\frac{1}{2}\left(\sin(x-y)+\sin(x+y)\right) chun an toradh a fháil.

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

Dealaigh 240 ó 135. Suimigh 240 le 135?

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

Déan áirimh.

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

Comhcheangail -\frac{1}{4}\sqrt{2} agus -\frac{1}{4}\sqrt{2} chun -\frac{1}{2}\sqrt{2} a fháil.

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

Méadaigh 4 agus -\frac{1}{2} chun -2 a fháil.

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

Faigh luach do\sin(45)ón dtábla luachanna triantánúla.

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

Cealaigh 2 agus 2.

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

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$-2$$