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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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