Complete the identity. cos ⁡ 4 x − cos ⁡ 8 x cos ⁡ 4 x + cos ⁡ 8 x

Question

Complete the identity.             cos      ⁡      4      x      −      cos      ⁡      8      x              cos      ⁡      4      x      +      cos      ⁡      8      x

Brenton Gay · Accepted Answer

Complete the identity.             cos      ⁡      4      x      −      cos      ⁡      8      x              cos      ⁡      4      x      +      cos      ⁡      8      x        cos  ⁡  p  +  cos  ⁡  q  =  2  cos  ⁡      1    2    (  p  +  q  )  cos  ⁡      1    2    (  p  −  q  )  cos  ⁡  p  −  cos  ⁡  q  =  −  2  sin  ⁡      1    2    (  p  +  q  )  sin  ⁡      1    2    (  p  −  q  )  sin  ⁡  (  −  x  )  =  −  sin  ⁡  x  cos  ⁡  (  −  x  )  =  cos  ⁡  x            cos      ⁡      4      x      −      cos      ⁡      8      x              cos      ⁡      4      x      +      cos      ⁡      8      x        =            −      2      sin      ⁡              1        2            (      4      x      +      8      x      )      sin      ⁡              1        2            (      4      x      −      8      x      )              2      cos      ⁡              1        2            (      4      x      +      8      x      )      cos      ⁡              1        2            (      4      x      −      8      x      )        =            sin      ⁡      6      x      sin      ⁡      2      x              cos      ⁡      6      x      cos      ⁡      2      x        =  tan  ⁡  6  x  ∗  tan  ⁡  2  x

Complete the identity. (cos 4x-cos 8x)/(cos 4x+ cos 8x)

Answered question

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