cosAcos(3π−A)cos(3π+A)=1/4 cos3A
Answers
Answer:
if this is the question of Prove then the solution is
CosA . Cos(π/3-A).cos(π/3+A)=1/4cos3A
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cos(π/3 - A) = cos(π/3)cosA + sin(π/3)sinA
= (1/2)cosA + (√3/2)sinA
Similarly,
cos(π/3 + A) = (1/2)cosA - (√3/2)sinA
So,
cosAcos(π/3-A)cos(π/3+A) = cosA[(1/4)cos2A - (3/4)sin2A]
= cosA[(1/4)cos2A - (3/4)(1-cos2A)]
= cosA[cos2A - 3/4]
= (1/4)(4cos3A - 3cosA) =(1/4)cos(3A)
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NOTE: cos(3A) = cos(2A+A) = cos(2A)cosA - sin(2A)sinA
= (2cos2A-1)cosA -2sinAcosAsinA
= 2cos3A-cosA - 2sin2AcosA
= 2cos3A - cosA - 2(1-cos2A)cosA
= 4cos3A - 3cosA