Bài tập 4. Tính giá trị của các biểu thức sau (không dùng máy tính cầm tay):
a. $A=\cos 0^{\circ}+\cos 40^{\circ}+\cos 120^{\circ}+\cos 140^{\circ}$;
b. $B=\sin 5^{\circ}+\sin 150^{\circ}-\sin 175^{\circ}+\sin 180^{\circ}$;
c. $C=\cos 15^{\circ}+\cos 35^{\circ}-\sin 75^{\circ}-\sin 55^{\circ}$;
d. $D=\tan 25^{\circ} \cdot \tan 45^{\circ} \cdot \tan 115^{\circ}$;
e. $E=\cot 10^{\circ} \cdot \cot 30^{\circ} \cdot \cot 100^{\circ}$.
Bài Làm:
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. $E=\cot 10^{\circ} \cdot \cot 30^{\circ} \cdot \cot 100^{\circ}$
$=\cot (90^{\circ}-80^{\circ}) \cdot \cot 30^{\circ} \cdot \cot (180^{\circ}-80^{\circ})$
$=\tan80^{\circ} \cdot \cot 30^{\circ} \cdot (-\cot 80^{\circ})$
$=- \cot 30^{\circ}$
$=-\sqrt{3}$