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prove that tan20 .tan40.tan80=tan60.

Dear Student!!

@Vaibhav: Correct answer..!! Well Done..!!

Keep posting..!

Here is a thumps up for you.

 

Cheers..!

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 tan40.tan20.tan80 = tan60

   Taking L.H.S.

   tan40.tan80.tan20

=(sin40 sin80)sin20/cos40 cos80(cos20)

=(2sin40 sin80) sin20 / (2cos40 cos80)cos20

=(cos40- cos120) sin20 / (cos120 + cos40) cos20

=(2cos40 + 1)sin20 /  (2cos40 - 1) cos20

=2cos40sin20 + sin20 / 2cos40cos20 - cos20

=sin60 - sin20 + sin20 / cos60 + cos20  - cos20

=sin60/cos60

=tan60 = R.H.S.

Cheers . 

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