SIMPLIFYING TRIG EXPRESSIONS USING IDENTITIES WORKSHEET

Simplify.

Problem 1 :

tan x(csc x - sin x)

Solution

Problem 2 :

(csc x - 1) (csc x + 1)

Solution

Problem 3 :

(sec x - tan x) (sec x + tan x)

Solution

Problem 4 :

(1 + tan2x) (1 - sin2x)

Solution

Problem 5 :

cos x(csc x - secx) - cot x

Solution

Problem 6 :

sin2 x(cot2x + 1)

Solution

Problem 7 :

sin2x + sin2x cot2x

Solution

Problem 8 :

cot x sec x sin x

Solution

Problem 9 :

cot2x/(cscx - 1)

Solution

Answer Key

1) cos x

2)  cot2x

3)  1

4)  1

5)  -1

6)  1

7)  1

8)  1

9) (1 + sin x)/ sinx

Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant.

Problem 1 :

cot ฮธ sin ฮธ

Solution

Problem 2 :

1 - sin2๐œƒsin2๐œƒ

Solution

Problem 3 :

sin ฮธ sec ฮธ

Solution

Problem 4 :

cos ๐œƒ csc ๐œƒ cot ๐œƒ

Solution

Problem 5 :

sec ๐œƒ tan ๐œƒ

Solution

Problem 6 :

1 - sin2๐œƒcot2๐œƒ

Solution

Problem 7 :

sin ๐œƒ csc ๐œƒ cot ๐œƒ

Solution

Problem 8 :

cos ฮธ/sec ฮธ

Solution

Problem 9 :

tan ๐œƒ + cot ๐œƒ tan ๐œƒ

Solution

Problem 10 :

cos2๐œƒ1 - sin ๐œƒ

Solution

Problem 11 :

sec2๐œƒ - 1sec2๐œƒ

Solution

Problem 12 :

tan ฮธ csc ฮธ cos ฮธ

Solution

Answer Key

1)  cos ฮธ

2)  cot2ฮธ

3)  tan ฮธ

4)  1

5)  csc ฮธ

6)  sin2 ฮธ

7) tan ฮธ

8)  cos2ฮธ

9) csc2 ฮธ

10)  1+ sinฮธ

11) sin2 ฮธ

12)  1

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