Question

Prove that cos20°cos30°cos40°cos80°=√3/16

Answer 1

Answer:

it's proved that cos 20°cos 30° cos40° cos80° =√3/16

Step-by-step explanation:

cos 20 cos 30 cos 40 cos 80

= cos 20 (√3 /2) cos 40 cos 80 [ cos 30 = (√3 /2) ]

= (√3 /4) cos 20 (2cos 80 cos 40)

= (√3 /4) cos 20 { cos 120 + cos 40 } [ 2cos a cos b = cos (a+b) + cos (a-b) ]

= (-√3 /8) cos 20 + (√3 /4) cos 40 cos 20 [cos 120 = -1/2 ]

= (-√3 /8) cos 20 + (√3 /8) 2 cos 40 cos 20

= (-√3 /8) cos 20 + (√3 /8) cos 60 + (√3 /8) cos20

= (√3 /8).(1/2)

= √3 /16

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