Buktikan bahwa sin 20*sin40+sin60*sin80=3/16.

Penyelesaian:

Pertimbangkan LHS

sin 20 × sin 40 × sin60 × sin80

Nilai sin

sin 0° = (0/4) = 0

sin 30° = (1/4) =

sin 45° = (2/4) = 1/√2

sin 60° = 3/4 = 3/2

sin 90° = (4/4) = 1

LHS = sin60 [sin20 × sin40 × sin80]

LHS = 3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

LHS = 3/2[sin 3(20)/4]

LHS = 3/2[sin 60/4]

LHS = 3/2[√3/2 × 4]

LHS = 3/2 × 3/8

LHS = 3/16

LHS = RHS

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