1. Jika secan x + tan x = 3/2 dan 0 ≤ x ≤ π/2, maka nilai sin x = ....?

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Sec x + Tan x = 3/2
(Sec x + Tan x)(Sec x - Tan x) = 3/2(Sec x - Tan x)
Sec²x - Tan²x = 3/2(Sec x - Tan x)
1 = 3/2(Sec x - Tan x)
Sec x - Tan x = 2/3

Eliminasi...
Sec x + Tan x = 3/2
Sec x - Tan x = 2/3
——————————— (-)
2Tan x = 3/2 - 2/3
2Tan x = (9 - 4)/6
2Tan x = 5/6
Tan x = 5/12

Ingat !
Tan x = Depan/Samping

Didapat :
Depan = 5
Samping = 12
Miring = 13 (Triple Pythagoras)

Maka...
Sin x = Depan/Miring
Sin x = 5/13

Bab Trigonometri
Matematika SMA Kelas X

sec x + tan x = 3/2
sec x + (sin x / cos x) = 3/2
(cos x . sec x + sin x)/cos x = 3/2
(1 + sin x)/cos x = 3/2
2 (1 + sin x) = 3 . cos x
2 + 2 sin x = 3 (√(1 - sin² x)
**kuadratkan**
(2 + 2 sin x)² = 9 . (1 - sin² x)
4 + 8 sin x + 4 sin² x = 9 - 9 sin² x
9 sin² x + 4 sin² x + 8 sin x + 4 - 9 = 0
13 sin² x + 8 sin x - 5 = 0
(13 sin x - 5) (sin x + 1) = 0
13 sin x - 5 = 0
sin x = 5/13

atau

sin x + 1 = 0
sin x = - 1