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

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

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

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

$= \frac{1}{2}$

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

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

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

$= 0$

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

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

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

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

$= - 1$

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

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

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

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

$= - \sqrt{3}$