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Cos π/15 *cos2π/15*cos3π/15*cos4π/15cos 5π/15*cos6π/15 *cos7π/15= 1/128

Cos π/15 *cos2π/15*cos3π/15*cos4π/15cos 5π/15*cos6π/15 *cos7π/15= 1/128

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
= (1/16) * (1/4) * (1 / 2) = 1/128Therefore, the left sin (4π / 5) = sin (π / 5) Note that sin (16π / 15) = - sin (π / 15) (4π / 5) / [4sin (π / 5)]} * (1/2) (using the conclusion (1) (1) 2)) = - [cos (π / 15 ) cos (2π / 15) cos (4π / 15) cos (8π / 15)] * [cos (π / 5) cos (2π / 5)] * (1/2)then left the formula cos (5π / 15) = cos ( π / 3) = 1/2 cos (6π / 15) = cos (2π / 5) cos (3π / 15) cos (π / 5) cos (7π / 15) = cos (8π / 15) cos (2π / 15) cos (4π / 15) cos (7π / 15) * [cos (3π / 15) cos (5π / 15) cos (6π / 15) = cos (π / 15) cos (2π / 15) cos (3π / 15) cos (4π / 15) cos (5π / 15) cos (6π Cos (7π / 15) then left the formula = sin16x / [16sinx] = 2sin8xcos8x / [16sinx] = 4sin4xcos4xcos8x / [16sinx ] = 8sin2xcos2xcos4xcos8x / [16sinx] = 16sinxcosxcos2xcos4xcos8x / [16sinx] (2) cosxcos2xcos4xcos8x = sin4x / [4sinx] = 2sin2xcos2x / [4sinx] = 4sinxcosxcos2x / [4sinx] (1) cosxcos2x The following two conclusions are noted:

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