Question

Jika tan 1/2α = 1/2, hitunglah nilai sin2α
Tolong dong!

Answer 1

Diketahui  tan 1/2 A = 1/2
misal tan 1/2 A = y/x = 1/2 dan anggap A lancip
r=√(x²+y²)
r= √(2²+1²)
r = √5

sin 1/2 A = y/r = 1/√5 = (1/5)√5
cos 1/2A= x/r = 2/√5 = (2/5)√5

sin A = 2 sin 1/2 A cos 1/2A
sin A = 2(1/5)√5.(2/5)√5
sin A = 4/5
cos A = √(1-sin² A) = 3/5

sin 2A = 2 sin A cos A
sin 2A = 2 (4/5)(3/5) 
sin 2A = 24/25