Nilai (cosec 420 cos 1.110/tan 570=....

sqrt(3)

Pembahasan

Untuk menyelesaikan soal ini, kita perlu menghitung nilai dari ekspresi trigonometri tersebut:

cos(420) = cos(420 - 360) = cos(60) = 1/2
cos(1110) = cos(1110 - 3 * 360) = cos(1110 - 1080) = cos(30) = sqrt(3)/2
tan(570) = tan(570 - 360) = tan(210) = tan(180+30) = tan(30) = 1/sqrt(3)

cosec(420) = 1/sin(420) = 1/sin(60) = 1/(sqrt(3)/2) = 2/sqrt(3)

Jadi, (cosec 420 * cos 1110) / tan 570 = ( (2/sqrt(3)) * (sqrt(3)/2) ) / (1/sqrt(3))
                                              = 1 / (1/sqrt(3))
                                              = sqrt(3)