Rut gon cos(a + b + c) + cos(b + c – a) +cos(c + a – b) + cos(a + b – c) hua 5* va cam on

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1. cos(a + b + c) + cos(b + c – a) + cos(c + a – b) + cos(a + b – c)

   = 2cos(b + c).cosa + 2cosa.cos(c – b)

   = 2cosa(cos(b + c) + cos(c – b))

   = 4cosa.cosb.cosc

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2. cos(a + b + c) + cos(b + c – a) + cos(c + a – b) + cos(a + b – c)

   = (cos(a + b + c) + cos(b + c – a)) + (cos(c + a – b) + cos(a + b – c))

   = 2 × cos((a + b + c + b + c – a)/2) × cos((a + b + c – b – c + a/2) + 2 × cos((c + a – b + a + b – c)/2) × cos((c + a – b – a – b + c)/2)

   = 2 × cos((2b + 2c)/2) × cos(2a/2) + 2 × cos(2a/2) × cos((2c – 2b)/2)

   = 2 × cos(b + c) × cosa + 2 × cosa × cos(c – b)

   = 2 × cosa × (cos(b + c) + cos(b – c))

   = 2 × cosa × ((cosb × cosc – sinb × sinc) + (cosb × cosc + sinb × sinc))

   = 2 × cosa × 2(cosb × cosc)

   = 4 × cosa × cosb × cosc

   GOOD LUCK!

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