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Exercise #17
Sum and Difference Identities II


                
Express cos   x  as a function of x only.
            2    




Therefore, we can use the sum and difference identities when proving identities.

Example
               1          3
Prove sin  x    sin x     cos x .
              3 2         2




Working Backwards
Evaluate without using a calculator:

                      5          5
       sin       cos       cos sin
             9         36      9    36
Try
Find the exact value of:

                                             
        cos        cos        sin        sin
              12         3           12         3




Example
Prove that sin(   )  sin(   )  2cos  sin  .




Journal
                              4                                            5               3
Given that tan               where  is not in quadrant IV and cot      where        ,
                              3                                           12                2
find cos(   ) .

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Exercise #17 notes

  • 1. Exercise #17 Sum and Difference Identities II   Express cos   x  as a function of x only. 2  Therefore, we can use the sum and difference identities when proving identities. Example   1 3 Prove sin  x    sin x  cos x .  3 2 2 Working Backwards Evaluate without using a calculator:  5  5 sin cos  cos sin 9 36 9 36
  • 2. Try Find the exact value of:     cos cos  sin sin 12 3 12 3 Example Prove that sin(   )  sin(   )  2cos  sin  . Journal 4 5 3 Given that tan    where  is not in quadrant IV and cot   where     , 3 12 2 find cos(   ) .