sin(π/7)sin(2π/7)sin(4π/7)=?
sheershaka:
Is the answer -1/8
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Answered by
14
sin A sin B = 1/2 [ cos A-B - Cos A+B ]
sin A cos B = 1/2 [ sin A+B + sin A-B ] also sin Ф = sin π - Ф
sin 4π/7 = sin (π - 4π/7) = Sin 3π/7
Sin π/7 Sin 4π/7 = Sin π/7 Sin 3π/7 = 1/2 [ cos 2π/7 - cos 4π/7 ]
Sin π/7 Sin 4π/7 Sin 2π/7 = 1/2 [ Sin 2π/7 Cos 2π/7 - Sin 2π/7 Cos 4π/7 ]
= 1/2 1/2 [ Sin 4π/7 + Sin 0 - (Sin 6π/7 + Sin -2π/7 ) ]
= 1/4 [ Sin 4π/7 - sin π/7 + sin 2π/7 ]
sin A cos B = 1/2 [ sin A+B + sin A-B ] also sin Ф = sin π - Ф
sin 4π/7 = sin (π - 4π/7) = Sin 3π/7
Sin π/7 Sin 4π/7 = Sin π/7 Sin 3π/7 = 1/2 [ cos 2π/7 - cos 4π/7 ]
Sin π/7 Sin 4π/7 Sin 2π/7 = 1/2 [ Sin 2π/7 Cos 2π/7 - Sin 2π/7 Cos 4π/7 ]
= 1/2 1/2 [ Sin 4π/7 + Sin 0 - (Sin 6π/7 + Sin -2π/7 ) ]
= 1/4 [ Sin 4π/7 - sin π/7 + sin 2π/7 ]
Answered by
1
Answer:
√7/8
I think, it will help you
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