cos10.cos20.cos40 is equal to
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Step-by-step explanation:cos a cos 2a cos 2^
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Step-by-step explanation:
=[1/(2sin10)]*2sin10*cos10*cos20*cos40
=[1/(4sin10)]*2sin20*cos20*cos40
=[1/(8sin10)]*2sin40*cos40
=[1/(8sin10)]*sin80
=1/8*1/sin10*cos10 [ sin80=sin(90–10)=cos10]
=1/8*cot10
OR
Let y = Cos(10)*Cos(20)*Cos(40)
So y = Sin(10)*Cos(10)*Cos(20)*Cos(40)/Sin(10)
=2*Sin(10)*Cos(10)*Cos(20)*Cos(40)/2*Sin(10)
As 2 * Sin(A)*Cos(A) = Sin(2*A)
So, y = Sin(20)*Cos(20)*Cos(40)/2*Sin(10)
= 2*Sin(20)*Cos(20)*Cos(40)/4*Sin(10)
By same analogy as above we have,
y = Sin(40)*Cos(40)/4*Sin(10)
= 2*Sin(40)*Cos(40)/8*Sin(10)
By same analogy as previous we have,
y = Sin(80)/8*Sin(10)
As Sin(A) = Cos(90 - A)
So, y = Cos(90 - 80)/8*Sin(10)
=Cos(10)/8*Sin(10)
= Cot(10)/8
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