Question

Prove the following?
cos7x+cos5x+cos3x+cosx=4cosxcos2xcos4x

Answer 1

LHS=cos7x + cos5x + cos3x + cosx 
=2cos[(7x+5x)/2].cos[(7x-5x)/2] + 2cos[(3x+x)/2].cos[(3x-x)/2]  
  [∵ cosA + cosB = 2.cos[(A+B)/2].cos[(A-B)/2]]
=2cos[(12x)/2].cos[(2x)/2] + 2cos[(4x)/2].cos[(2x)/2]
=2cos 6x.cosx+2cos2x.cosx                                                                           
=2cosx(cos 6x+ cos 2x)
=2.cosx(2cos[(6x+2x)/2].cos[(6x-2x)/2]
=2.cosx(2cos4x.cos2x)
=4.cosx.cos2x.cos4x
=RHS.

Answer 2

find ur ans attached here......

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