Solution To Advanced Exercise Number Three

ADVANCED EXERCISES

(3) Simplify.

 (a)       e
     -------------
      (e^{sin x})^{sin x}

 (b) sin²(e^x) + cos²(e^x)

 (c)

SOLUTION:

 (a)       e            e            e
     ------------- = -------- = ------------
      (e^{sin x})^{sin x}     e^sin²x      e^{1 - cos²x}

   = e^{1 - (1 - cos²x)} = e^{1 - 1 + cos²x} = e^cos²x


 (b) sin²(e^x) + cos²(e^x) = 1

 (c)  =  = e^x + 1

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