prove that cos 10.cos30.cos50.cos70 = 3/16

cos30.(cos50cos10).cos70

= root3/2 .1/2(2cos10cos50)cos70

= root3/2 .1/2 (cos60 + cos40 ).cos70.............[ bcoz 2cosxcosy = cos(x+y) + cos(x-y) ]

= root3/4 (cos60.cos70 + cos40cos70)

= root3/8 [ cos70 + 2cos40cos70 ]

= root3/8 [ cos70 + cos110 + cos30 ]

= root3/8 [ cos70 - cos70 + root3/2]

= root3/8 . root3/2

= 3/16

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