Proving cos ⁡ θ sin ⁡ θ ( sin 2 ⁡ θ − cos 2 ⁡ θ ) = − sin ⁡ 4 θ 4 In simplifying this do they take the negative out of ( sin 2 ⁡ θ − cos 2 ⁡ θ ) to get − cos ⁡ θ sin ⁡ θ = − sin ⁡ 4 θ 4

Question

Proving   cos  ⁡  θ  sin  ⁡  θ  (      sin    2    ⁡  θ  −      cos    2    ⁡  θ  )  =  −            sin      ⁡      4      θ        4  In simplifying this do they take the negative out of   (      sin    2    ⁡  θ  −      cos    2    ⁡  θ  ) to get  −  cos  ⁡  θ  sin  ⁡  θ  =  −            sin      ⁡      4      θ        4

Stacy Johns · Accepted Answer

Heres a complete answer  cos  ⁡  θ  sin  ⁡  θ  (      sin    2    ⁡  θ  −      cos    2    ⁡  θ  )  =            sin      ⁡      (      2      θ      )        2    ∗  −  cos  ⁡  (  2  θ  )Again,            −      sin      ⁡      (      2      θ      )      cos      ⁡      (      2      θ      )        2    =            −      sin      ⁡      (      4      θ      )        4  I mainly used these two relation      cos    2    ⁡  (  x  )  −      sin    2    ⁡  (  x  )  =  cos  ⁡  (  2  x  )which gives      sin    2    ⁡  (  x  )  −      cos    2    ⁡  (  x  )  =  −  cos  ⁡  (  2  x  )and  sin  ⁡  (  2  θ  )  =  2  sin  ⁡  (  θ  )  cos  ⁡  (  θ  )which gives            sin      ⁡      (      2      θ      )        2    =  sin  ⁡  (  θ  )  cos  ⁡  (  θ  )Similarly            sin      ⁡      (      4      θ      )        2    =  sin  ⁡  (  2  θ  )  cos  ⁡  (  2  θ  )

Proving cos ⁡ θ sin ⁡ θ<!-- θ

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