Rút gọn
1. A= cos160° + cos20° + sin30°
2. B= sin(-40°) + sin40° +sin²40° + cos²40°
3. C= cos²50° + cos²40° – tan10°. tan80°
Rút gọn 1. A= cos160° + cos20° + sin30° 2. B= sin(-40°) + sin40° +sin²40° + cos²40° 3. C= cos²50° + cos²40° – tan10°. tan80°
By Daisy
1.
$A=\cos 160^o+\cos 20^o+\sin 30^o$
$=2\cos 90^o.\cos 70^o+\sin 30^o$
$=\sin 30^o$
2.
$B=\sin(-40^o)+\sin 40^o + \sin^240^o+\cos^240^o$
$= 0+1=1$
3.
$C=\cos^250^o+\cos^240^o-\tan 10^o.\tan 80^o$
$= \cos^250^o+\sin^250^o-\tan 10^o.\cot 10^o$
$= 1-1=0$
Đáp án:
Giải thích các bước giải:
1.A=$2\cos \frac{160^{\circ}+20^{\circ}}{2}.\cos \frac{160^{\circ}-20^{\circ}}{2}+\sin 30^{\circ}=-2\cos 90^{\circ}.\cos 70^{\circ}+\sin 30^{\circ}=\sin 30^{\circ}=\frac{1}{2}$
2.B=$(-\sin 40^{\circ}+\sin 40^{\circ})+(\sin ^{2}40^{\circ}+\cos ^{2}40^{\circ})=0+1=1$
3.C=$\frac{1+\cos 100^{\circ}}{2}+\frac{1+\cos 80^{\circ}}{2}-\frac{\sin 10^{\circ}.\sin 80^{\circ}}{\cos 10^{\circ}.\cos 80^{\circ}}$
=$\frac{1+\cos 100^{\circ}}{2}+\frac{1+\cos 80^{\circ}}{2}-\frac{\frac{\cos 70^{\circ}}{2}}{\frac{\cos 70^{\circ}}{2}}$
=$1+\frac{1}{2}.(\cos 100^{\circ}+\cos 80^{\circ})-1$
=$\frac{1}{2}.2.\cos 90^{\circ}.\cos 10^{\circ}=0$