Question

prove that cos20.cos40.cos60.cos80=1/6​

Answer 1

Answer:

Cos20cos40cos60cos80=1/6

multiply both sides by sin20

sin20cos20cos40cos60cos80=asin20

By double angle formula,

#sin20cos20=1/2sin40

We can continue this pattern.

1/2sin40cos40cos60cos80=asin20

1/4sin80cos80cos60=asin20

1/8sin160cos60=asin20

cos60 is simply 1/2

So,

1/16sin160=asin20

However,

sin160=sin20

So, a=1/16

HENCE PROVED

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Answer 2

Answer:

your answer attached in the photo