Question

Cos 10 into cos 30 into cos 50 into cos 70 is equal to 3 by 16 prove that

Answer 1

Hii There!!

Given that, cos10.cos30.cos50.cos70 = 3/16

Consider L.H.S. =) cos30.cos10.cos50.cos70

  =) root(3)/2 × cos10.cos50.cos70

  =) root(3)/4 × (cos60 + cos40)cos70

  =) root(3)/8 × 2cos60.cos70 + 2cos40.cos70

  =) root(3)/8 × (cos70 + cos110 + cos30)

  =) root(3)/8 × (cos70 - cos70 + root(3)/2)

  =) [root(3) × root(3)] / (8×2)

  =) 3/16 = R.H.S.



Hence,proved..

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