TRIG � Chapter 5 � Identities by DL45eFVt

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									Chipola College
Mac 1114
5.2b Verifying Trigonometric Identities__________________________________

A. Factor and simplify if possible.

1. cos2 x – cos x


2. tan2 x – cos2 x


3. 2 cos2 x – 5 cos x – 3


4. cos4 x - 2 cos2 x + 1


5. cos3 x – tan3 x


6. cos4 x – sin4 x


B. Use the Identities to Substitute into the following expressions so that the result is in
   terms of sine and cosine only. Where possible the answer should contain no parentheses
   or fractions.

      csc x sec x                                               1  sin 2 
 7.                                                        8.
        cot x                                                   1  cot 2 




      1  tan 2 
 9.
      1  cot 2 



C. Use trig substitutions to rewrite each function in terms of the function requested.


  10. cos x, in terms of sin x                            11. cos x, in terms of tan x
D. Verifying trigonometric identities.

      Hints:     Substitute basic identities equivalences
                 Perform algebra (reduce fractions, add fractions, factor, etc.)
                 Rewrite everything in terms of sine and cosine

       tan                                                   tan 2 x  1
12.           sin                                     13.                sec x
       sec                                                     sec x




14. sin 2  1  cot 2    1
                                                                    1
                                                        15. 1       2
                                                                         sin 2 x
                                                                  sec x




You Try:

16. (sin x  cos x) 2  1  2 sin x cos x                         17. sin 4   cos4   2 sin 2   1

								
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