Question

Trigonometri kelas XI

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas XI

cos (x - y) = 1/2 . √3
cos x cos y + sin x sin y = 1/2 . √3
1/2 + sin x sin y = 1/2 . √3
sin x sin y = 1/2 . √3 - 1/2

cos (x + y)
= cos x cos y - sin x sin y
= 1/2 - (1/2 . √3 - 1/2)
= 1/2 - 1/2 √3 + 1/2
= 1 - 1/2 √3

(cos (x + y)) / (cos (x - y))
= (1 - 1/2 √3) / (1/2 √3)
= ((2 - √3)/2) : (1/2 √3)
= (2 - √3)/√3
= √3 (2 - √3)/3
= (2√3 - 3)/3

Answer 2

Verified answer

Jawab

cos(x-y) = 1/2 √3
cos x cos y + sin x sin y = 1/2 √3
1/2 + sin x sin y = 1/2 √3
sin x sin y = 1/2 √ 3 - 1/2 

cos (x+y) = cos x cos y - sin x sin y
= 1/2 - (1/2 √3 - 1/2)
=  1- 1/2 √3
= 1/2 (2 - √3)

cos (x+y) / cos (x-y) =
= 1/2 (2- √3) / 1/2 √3
=  (2 - √3) / (√3)
=  (2 - √3)√3 /(3)
= 1/3 (2√3 - 3)