Verify this identity: sin ⁡ 6 α + sin ⁡ 2 α = cos 2 ⁡ 2 α − cos ⁡ 2 α cos ⁡ 6 α sin ⁡ 2 α

Question

Verify this identity:   sin  ⁡  6  α  +  sin  ⁡  2  α  =                    cos        2            ⁡      2      α      −      cos      ⁡      2      α      cos      ⁡      6      α              sin      ⁡      2      α

Guillemaejy9x · Accepted Answer

cos        2            ⁡      2      α      −      cos      ⁡      2      α      cos      ⁡      6      α              sin      ⁡      2      α        =            cos      ⁡      2      α      (      cos      ⁡      2      α      −      cos      ⁡      6      α      )              sin      ⁡      2      α                              =            2      cos      ⁡      2      α      (      sin      ⁡      2      α      ×      sin      ⁡      4      α      )              sin      ⁡      2      α                  =  2  cos  ⁡  2  α  sin  ⁡  4  α                    =  sin  ⁡  6  α  +  sin  ⁡  2  α

Sabrina Burgess · Accepted Answer

The identity is equivalent (for   sin  ⁡  2  α  ≠  0) to      sin    2    ⁡  2  α  +  sin  ⁡  2  α  sin  ⁡  6  α  −      cos    2    ⁡  2  α  +  cos  ⁡  2  α  cos  ⁡  6  α  =  0Note that  cos  ⁡  2  α  cos  ⁡  6  α  +  sin  ⁡  2  α  sin  ⁡  6  α  =  cos  ⁡  (  6  α  −  2  α  )  =  cos  ⁡  4  αand      cos    2    ⁡  2  α  −      sin    2    ⁡  2  α  =  cos  ⁡  4  α

Verify this identity: sin ⁡ 6 α + sin &#x206

Answered question

Answer & Explanation

New Questions in Trigonometry