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How transform in product `cos((3x)/2)+cos((7x)/2)+cosx` ?

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xalal | (Level 1) Honors

Posted July 3, 2013 at 5:26 PM via web

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How transform in product `cos((3x)/2)+cos((7x)/2)+cosx` ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 3, 2013 at 5:35 PM (Answer #1)

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The sum `cos((3x)/2)+cos((7x)/2)+cosx` has to be transformed to product form.

`cos((3x)/2)+cos((7x)/2)+cosx`

= `2*cos(((3x)/2+(7x)/2)/2)*cos(((3x)/2-(7x)/2)/2) + cos x `

= `2*cos((10x)/4)*cos((-4x)/4) + cos x`

= `2*cos ((5x)/2)*cos -x + cos x`

= `cos x*(1 - 2*cos ((5x)/2))`

The product form is `cos x*(1 - 2*cos ((5x)/2))`

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