Cos 110 + cos 50 / sin 110 - sin 50

jawab

(cos 110 + cos 50) / (sin 110 - sin 50)
= { 2cos 1/2 (110+50) cos 1/2 (110-50)} /(2cos 1/2 (110+50) sin 1/2(110-50)}
= (2 cos 1/2(160)cos 1/2 (60)} / (2 cos 1/2(160)sin 1/2 (60)
= (2 cos 80 cos 30)  / (2 cos 80  sin 30)
= cos  30/sin 30
= (1/2 √3)/ (1/2)
= √3

TriGonoMetRi

cos a + cos b = 2 cos (a+b)/2 cos (a-b)/2
sin a - sin b = 2 cos (a+b)/2 sin (a-b)/2

••
a = 110
b = 50

cos 110 cos 50 / sin 110 - sin 50
= 2 cos 80 cos 30 / 2 cos 80 sin 30
= cos 30 / sin 30
= 1/tan 30
= 1/(1/√3)
= √3