Simplifying Trigonometric Expressions

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Show your work for each problem.

1.
Which expression is equal to $\cos x \tan x$ ?
1. a) $\sec x$
2. b) $\sin x$
3. c) $\cos^2 x$
4. d) $1$
2.
Simplify $1 - \sin^2 x$ .
1. a) $\cos^2 x$
2. b) $\tan^2 x$
3. c) $-\cos^2 x$
4. d) $\sec^2 x$
3.
Simplify $\tan x \cot x + 4$ . The result is a number: what is it?
4.
Simplify $\csc x \tan x$ .
5.
Simplify $\cot x \cdot \sin x \cdot \sec x$ .
6.
A student simplified $\dfrac{\sin x}{\tan x}$ to $\sin^2 x$ . Check this at $x = 60°$ . Then find the correct simplified form.
7.
Simplify $\dfrac{\sec x}{\csc x}$ .
1. a) $\tan x$
2. b) $\sin x \cos x$
3. c) $\cot x$
4. d) $1$
8.
Simplify $\sec^2 x - \tan^2 x + \csc^2 x - \cot^2 x$ . The result is a number: what is it?
9.
Simplify $\dfrac{\sin x}{\csc x} + \dfrac{\cos x}{\sec x}$ .
10.
Simplify $\dfrac{1 - \cos^2 x}{1 - \sin^2 x}$ .
1. a) $-1$
2. b) $\cot^2 x$
3. c) $1$
4. d) $\tan^2 x$
11.
The expression $\dfrac{4 - 4\cos^2 x}{\sin x}$ simplifies to $k\sin x$ . What is $k$ ?
12.
Simplify $\dfrac{\sin^2 x}{1 - \cos x}$ , then evaluate the result at $x = 60°$ .
13.
Simplify $\sin x - \sin x \cos^2 x$ and evaluate it at $x = 30°$ .
14.
Simplify $\dfrac{\cos x}{1 - \sin x} - \dfrac{\cos x}{1 + \sin x}$ .
1. a) $2\cot x$
2. b) $0$
3. c) $2\tan x$
4. d) $2\sec x$
15.
Simplify $\dfrac{1}{1 - \sin x} + \dfrac{1}{1 + \sin x}$ and evaluate the result at $x = 60°$ .
16.
Simplify $\dfrac{\tan^2 x}{\sec x + 1}$ , then evaluate the result at $x = 60°$ .
17.
Simplify $(\sin x + \cos x)^2 + (\sin x - \cos x)^2$ .
18.
Simplify $\dfrac{\tan x + \cot x}{\sec x \csc x}$ . The result is a number: what is it?