Question

cos 10° cos 20° cos 40°
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Answer 1

Answer:

you have values of theta

Answer 2

Answer:

Cot(10)/8

Explanation:

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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