Free Printable Trig Identities

1.

$\tan\theta\ =$

a)

$\frac{\sin\theta}{\cos\theta}$

b)

$\frac{\cos\theta}{\sin\theta}$

c)

$\frac{1}{\cos\theta}$

d)

$\cot\theta$

2.

$\sin^2\theta\ +\ \cos^2\theta\ =\ 1$

Solve for $\cos^2\theta$ .

a)

$\cot^2\theta+1$

b)

$\sec^2\theta-1$

c)

$\tan\theta+1$

d)

$1-\sin^2\theta$

3.

$\tan\theta\cos\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

4.

$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:

a)

$\cos^2\theta$

b)

$\sin^2\theta$

c)

$\sec^2\theta$

d)

$\tan^2\theta$

5.

$\cos\theta\ \csc\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

6.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

7.

Simplify

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

a)

$\sec\theta$

b)

$\cos^2\theta$

c)

$\sin^2\theta$

d)

$\frac{\sin^2\theta}{\cos^2\theta}$

8.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

9.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

$2\sec\theta$

b)

$\cot^2\theta$

c)

$\tan^2\theta$

d)

$\sec^2\theta+1$

10.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

11.

Simplify $\tan x\left(\cot x\ +\ \csc x\right)$

a)

$1\ +\ \sec x$

b)

$1\ +\ \csc x$

c)

$\sec x-1$

d)

$\tan^2x$

12.

$\frac{1-\cos^2\theta}{\tan^2\theta}$ can be simplified as

a)

$\cot^2\theta$

b)

$\tan^2\theta$

c)

$\sin^2\theta$

d)

$\cos^2\theta$

13.

What happens when you multiply two reciprocal functions?

a)

You get a pythagorean identity

b)

It equals 1

c)

You get a quotient identity

d)

It equals 0

14.

Which of the following would be a step to prove the following identity? $\csc x-\sec x=\frac{\cos x-\sin x}{\sin x\cos x}$

a)

$\frac{1}{\sin x}-\frac{1}{\cos x}$

b)

$\frac{\cos x-\sin x}{\sin x}$

c)

$\frac{\cos x-\sin x}{\cos x}$

d)

$\frac{1}{\sin x\cos x}$

15.

One step in proving the identity below would be:

\frac{\sec^2\theta-1}{\sec^2\theta}

a)

$\frac{\sec^2\theta}{\sec^2\theta}-\frac{1}{\sec^2\theta}$

b)

$\frac{\tan^2\theta}{\sec^2\theta}$

c)

Both A and B

d)

Neither A nor B

16.

$\frac{\tan\theta+\cot\theta}{\tan\theta}$ can be simplified as:

a)

$\csc^2\theta$

b)

$\cot^2\theta$

c)

$\sin^2\theta$

d)

$\cos^2\theta$

17.

$\sin\theta\cot\theta\ \sec\theta$

a)

$0$

b)

$1$

c)

$\sin\theta$

d)

$\cos\theta$

18.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

19.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

20.

Rewrite $\tan x$ in terms of $\sin x$ and $\cos x$

a)

$\tan x=\frac{\cos x}{\sin x}$

b)

$\tan x=\frac{1}{\cot x}$

c)

$\tan x=\frac{\sin x}{\cos x}$

d)

$\tan x=\frac{opposite}{adjacent}$

Trig Identities

Total questions: 20

Worksheet time: 2hrs 31mins

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