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Trigonometric Identities (Practice Problems)

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									Trigonometric Identities (Practice Problems)

   1. Simplify the expression:  sin x  cos x    sin x  cos x 
                                                   2                   2




   2. Simplify:       cosxcotx + sinx



                    sec x  csc x
   3. Simplify:
                      1  tan x




                   sec x tan x
   4. Simplify:         
                   cos x cot x




                       1  cos x     sin x
   5. Prove:                     
                         sin x     1  cos x




                                                1  sin x
   6. Prove:           secx + tanx + cotx =
                                               cos x sin x




                 cos  tan 
   7. What is                 cos 2  ?
                   sin 




   8. What is tan 2  cos2   1  sin 2  ?



   9. Simplify: cosxcscx
10.Simplify: secx – sinxtanx



                 tan x sin x
11.Simplify:
                  sec 2 x  1




               sin  sec 
12.Verify:                 1
                  tan 




13.Solve the following equations:
      a. 2sinx – 1 = 0


      b. sin x  2   sin x


      c. 2cos3x 1  0


      d. 2sin 2 x  sin x 1  0


      e. cot x cos2 x  2cot x


      f. 2tan x sin x  2sin x  tan x 1 (Hint: Factor by grouping)


      g. sin 2 x  3sin x  2  0 (Hint: Not Factorable…use the quadratic formula)


      h. sec2 x  2 tan x  4


      i.   sin x  tan x

								
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