Write the sum as a product. sin ⁡ ( 4 x ) − sin ⁡ ( 9 x )

Question

Write the sum as a product.  sin  ⁡  (  4  x  )  −  sin  ⁡  (  9  x  )

madirans2m · Accepted Answer

Solution: We know that   sin  ⁡  C  −  sin  ⁡  D  =  2  cos  ⁡  (            C      +      D        2    )  sin  ⁡  (            C      −      D        2    )Thus  sin  ⁡  (  4  x  )  −  sin  ⁡  (  9  x  )  =  2  cos  ⁡  (            4      x      +      9      x        2    )  sin  ⁡  (            4      x      −      9      x        2    )    =  2  cos  ⁡  (            13      x        2    )  sin  ⁡  (            −      5      x        2    )    =  −  2  cos  ⁡  (            13      x        2    )  sin  ⁡  (            5      x        2    )

Write the sum as a product. sin(4x) - sin(9x)

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