Free Printable Simplifying Trig Expressions with Identities

1.

Simplify the trig expression.

a)

secx

b)

cotx

c)

sec²x

d)

tan²x

2.

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

3.

a)

csc x

b)

sec x

c)

1/sec x

d)

cos x

4.

sec²(y) - tan²(y)

a)

tan(y)

b)

1

c)

-sin(y)

d)

-1

5.

(cot²x) / (cscx+1)

a)

cscx +1

b)

cscx−1

c)

secx−1

d)

secx+1

6.

Is this a pythagorean identity?
tan²x + 1 = secx

a)

Yes

b)

No

7.

a)

sin(x) - cos(x)

b)

-cot(x) - sec(x)

c)

cot(x) - sec(x)

d)

-sin(x) - cos(x)

8.

Simplify: $(\secθ-1)(\secθ+1)$

a)

sin ² θ

b)

cos ² θ

c)

tan ² θ

d)

sec ² θ

9.

Simplify: $\frac{\sec^2x}{\sec^2x-1}$

a)

$\sin^2x$

b)

$\csc^2x$

c)

$\cos^2x$

d)

$\sec^2x$

10.

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

a)

$\cot^2x$

b)

$\tan^2x$

c)

$\csc^2x$

d)

$\sec^2x$

11.

Simplify the trig expression.

a)

tan²x

b)

2

c)

cot²x

d)

1

12.

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

13.

Simplify:

csc(α)cos²(α) - csc(α)

a)

-1

b)

sin(α)

c)

-sin(α)

d)

tan(α)

14.

sin(x) tan(x) cot(x) csc(x)

a)

1

b)

sin(x)

c)

cos(x)

d)

tan(x)

15.

Simplify.
1/cos x

a)

sin x

b)

tan x

c)

sec x

d)

csc x

16.

-(sin²x + cos²x)

a)

-1

b)

1

c)

-2

d)

2

17.

Which of the following is not a pythagorean identity?

a)

cot²x + 1 = csc²x

b)

csc²x + 1 = cot²x

c)

cot²x - csc²x = -1

d)

csc²x - cot²x = 1

18.

$\frac{\tan x}{\sec x}$

a)

$\cos x$

b)

$\csc x$

c)

$\cot x$

d)

$\sin x\$

19.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

Show your work on paper!

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

20.

Simplify

$\cot\theta\sin\theta$

Show your work on paper!

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

Simplifying Trig Expressions with Identities

Total questions: 20

Worksheet time: 2hrs 6mins

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