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The gernal solution of the eqn Sinx + sin5x = sin 2x + sin4x

 The gernal solution of the eqn 
Sinx + sin5x = sin 2x + sin4x

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
sin x + sin 5x = sin 2x + sin 4x 
Express as a product. 
2 sin (6x/2)cos (4x/2) = 2 sin (6x/2)cos(2x)/2 
2 sin 3x cos 2x = 2 sin 3x cos x 
sin 3x = 0 
x = 0, π/3, 2π/3, π, 4π/3, 5π/3 
or cos 2x = cos x 
2 cos^2 x - 1 = cos x 
2 cos^2 x - cos x - 1 = 0 
(2 cos x + 1)(cos x -1) = 0 
cos x = -1/2 
x = 2π/3 etc. covered above. 
 
x = 2nπ ± 2π/3
 

cos x = 1 
x = 0, also covered above.
 
x = 2nπ
 
Regards
Arun (askIITians forum expert)

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