How can I express sin ⁡ 3 a sin ⁡ a while using only cos ⁡ a?

Question

How can I express                     sin        ⁡        3        a                    sin        ⁡        a             while using only   cos  ⁡  a?

Amy Daniels · Accepted Answer

We know that  sin  ⁡  3  a  =  sin  ⁡  (  2  a  +  a  )  =  …  =  3  sin  ⁡  a  −  4      sin    3    ⁡  aSo            sin      ⁡      3      a              sin      ⁡      a        =  3  −  4      sin    2    ⁡  a  =  3  −  4  +  4      cos    2    ⁡  a  =  4      cos    2    ⁡  a  −  1

cazinskup3 · Accepted Answer

sin      ⁡      3      a              sin      ⁡      a        =            3      sin      ⁡      a      −      4              sin        3            ⁡      a              sin      ⁡      a        =  3  −  4      sin    2    ⁡  a  =  3  −  4  (  1  −      cos    2    ⁡  a  )  =  3  −  4  +  4      cos    2    ⁡  a  =  4      cos    2    ⁡  a  −  1

How can I express sin ⁡ 3 a sin ⁡ a while using only cos...

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