Giải câu 4 bài giá trị lượng giác của một góc từ 0 đến 180 định lí côsin và định lí sin trong tam giác

a. $A=\cos 0^{\circ}+\cos 40^{\circ}+\cos 120^{\circ}+\cos 140^{\circ}$

$=\cos 0^{\circ}+\cos 40^{\circ}+\cos 120^{\circ}+\cos (180^{\circ}-40^{\circ})$

$=\cos 0^{\circ}+\cos 40^{\circ}+\cos 120^{\circ}-\cos 40^{\circ}$

$=\cos 0^{\circ}+\cos 120^{\circ}$

$=\frac{1}{2}$

b. $B=\sin 5^{\circ}+\sin 150^{\circ}-\sin 175^{\circ}+\sin 180^{\circ}$

$=\sin 5^{\circ}+\sin 150^{\circ}-\sin (180^{\circ}-5^{\circ})+\sin 180^{\circ}$

$=\sin 5^{\circ}+\sin 150^{\circ}-\sin5^{\circ}+\sin 180^{\circ}$

$=\sin 150^{\circ}+\sin 180^{\circ}$

$=\frac{1}{2}$

c. $C=\cos 15^{\circ}+\cos 35^{\circ}-\sin 75^{\circ}-\sin 55^{\circ}$

$=\cos 15^{\circ}+\cos 35^{\circ}-\sin (90^{\circ}-15^{\circ})^-\sin (90^{\circ}-35^{\circ})$

$=\cos 15^{\circ}+\cos 35^{\circ}-\cos15^{\circ}-\cos35^{\circ}$

$=0$

d. $D=\tan 25^{\circ} \cdot \tan 45^{\circ} \cdot \tan 115^{\circ}$

$=\tan (90^{\circ}-65^{\circ}) \cdot \tan 45^{\circ} \cdot \tan (180^{\circ}-65^{\circ})$

$=\cot65^{\circ} \cdot \tan 45^{\circ} \cdot (-\tan 65^{\circ})$

$=-\tan 45^{\circ} $

$=-1$

e. $E=\cot 10^{\circ} \cdot \cot 30^{\circ} \cdot \cot 100^{\circ}$

$=\cot (90^{\circ}-80^{\circ}) \cdot \cot 30^{\circ} \cdot \cot (180^{\circ}-80^{\circ})$

$=\tan80^{\circ} \cdot \cot 30^{\circ} \cdot (-\cot 80^{\circ})$

$=- \cot 30^{\circ}$

$=-\sqrt{3}$