prove that
sin12°sin48°sin54°=1/8
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Answered by
3
Answer:
sin(12°)sin(48°)sin(54°)
= [sin(12°)sin(48°)]sin(54°)
= sin(54°) * [cos(48° - 12°) - cos(48° + 12°)]/2
= sin(54°) * [cos(36°) - cos(60°)]/2
= sin(54°) * [cos(36°) - 1/2]/2
= cos(36°) * [cos(36°)/2 - 1/4]
= cos²(36°)/2 - cos(36°)/4.
Since cos(36°) = (1 + √5)/4:
cos²(36°)/2 - cos(36°)/4
= [(1 + √5)/4]²/2 - [(1 + √5)/4]/4
= (1 + √5)²/32 - (1 + √5)/16
= (6 + 2√5)/32 - (1 + √5)/16
= (6 + 2√5)/32 - (2 + 2√5)/32
= 4/32
= 1/8.
So sin(12°)sin(48°)sin(54°) = 1/8 follows.
please mark it as brainlist answer
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0
Answer:
oh vigorous
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