Tính:
A = sin15° + sin75° - cos15° - cos75° + sin30°
B = sin35° + sin67° - cos23° - cos55°
C = cos^2 20° + cos^2 40° + cos^2 50° + cos^2 70°
D = sin20° - tan40° + cot50° - cos70°
a) $A=\sin 15^{\circ}+\sin 75^{\circ}-\cos 15^{\circ}-\cos 75^{\circ}+\sin 30^{\circ}$
$=\cos 75^{\circ}+\cos 15^{\circ}-\cos 15^{\circ}-\cos 75^{\circ}+\sin 30^{\circ}$
$=\sin 30^{\circ}=\dfrac12$.
b) $B=\sin 35^{\circ}+\sin 67^{\circ}-\cos 23^{\circ}-\cos 55^{\circ}$
$=\cos 55^{\circ}+23^{\circ}-\cos 23^{\circ}-\cos 55^{\circ}$
$=0$
c) $C=\cos^2 20^{\circ}+\cos^2 40^{\circ}+\cos^2 50^{\circ}+\cos^2 70^{\circ}$
$=\sin^2 70^{\circ}+\sin^2 50^{\circ}+\cos^ 50^{\circ}+\cos^2 70^{\circ}$
$=(\sin^2 70^{\circ}+\cos^2 70^{\circ})+(\sin^2 50^{\circ}+\cos^ 50^{\circ})$
$=1+1=2$
d) $D=\sin 20^{\circ}-\tan 40^{\circ}+\cot 50^{\circ}-\cos 70^{\circ}$
$=\cos 70^{\circ}-\tan 40^{\circ}+\tan 40^{\circ}-\cos 70^{\circ}$
$=0$