Solve Sinx + Sin3x + Sin5x = 0.

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  • 117

 sin x + sin 3x + sin 5x

sin x + 2sin4x(-sin x)

sin x ( 1-2sin 4x)

sin x = 0     &       1- 2sin 4x = 0

                     &      2sin 4x = 1

                      &     sin 4x = 1/2

                         

                                             

  • -41

sinx + sin3x +sin5x = 0

sinx + 2sin4xcosx = 0

sinx + 2 x 2sin2x cos2x cosx =0

sinx +4 x 2 sinxcos2xcosx = 0

sinx(8cos2x cosx) = 0

sinx = 0

x = npi

8cos2xcosx = 0

cos2x = 0

2x = (2m + 1)pi/2

x = (2m+1)pi/4

cosx = 0

x = (2p+1)pi/2

  • 27
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