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If cos α + cos β + cos γ = 0, then prove that cos 3α + cos 3β + cos 3γ = 12 cos α cos β cos γ . |
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Answer» cos 3α + cos 3β + cos 3γ = (4 cos3α - 3 cos3α ) + (4 cos3 β – 3 cos β) + (4 cos3 γ – 3 cos γ) = 4(cos3 α + cos3 β + cos3 γ) – 3(cos α + cos β + cos γ) = 4(cos3 α + cos3 β + cos3 γ) – 3 × 0 = 4 (cos3 α + cos3 β + cos3 γ) = 4 × 3 cos α cos β cos γ (∵ a + b + c = 0 ⇒ a3 + b3 + c3 = 3abc) = 12 cos α cos β cos γ. |
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