Rewrite the expression as an equivalent expression that doesnot contain powers of trigonometric function greater than 1. cos ⁡ 3 x

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Rewrite the expression as an equivalent expression that doesnot contain powers of trigonometric function greater than 1.  cos  ⁡  3  x

sekanta2b · Accepted Answer

Rewrite the expression as anequivalent expression that does not contain powers of trigonometricfunction greater than 1.  cos  ⁡  3  x  =  cos  ⁡  (  2  x  +  x  )  =  cos  ⁡  2  x  cos  ⁡  x  −  sin  ⁡  2  x  sin  ⁡  x  =  (  2      cos          2        ⁡  x  −  1  )  cos  ⁡  x  −  2  sin  ⁡  x  cos  ⁡  x  sin  ⁡  x  =  2      cos          3        ⁡  x  −  cos  ⁡  x  −  2      sin          2        ⁡  x  cos  ⁡  x  =  2      cos          3        ⁡  x  −  cos  ⁡  x  −  2  (  1  −      cos          2        ⁡  x  )  cos  ⁡  x  =  2      cos          3        ⁡  x  −  cos  ⁡  x  −  2  cos  ⁡  x  +  2      cos          3        ⁡  x  =  4      cos          3        ⁡  x  −  3  cos  ⁡  x

abrigairaic · Accepted Answer

cos          3        ⁡  xif this is the case then you need to use the power reducing formula      cos          2        ⁡  u  =            1      −      cos      ⁡      2      u        2  Now,      cos          3        ⁡  x  =  (            1      −      cos      ⁡      2      x        2    )  (  cos  ⁡  x  )      cos          3        ⁡  x  =            cos      ⁡      x        2    −            (      cos      ⁡      2      x      )      cos      ⁡      x        2

Rewrite the expression as an equivalent expression that doesnot contain powers of trigonometric function greater than 1. cos 3x

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