Trigonometric Identities

Practice Questions

SAT Subject Test in Math I › Trigonometric Identities

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1

If $\sin \beta = \frac{3}{5}$ and $0 < \beta < \frac{\pi}{2}$ , evaluate $\cos 2\beta$ .

2

Using trigonometric identities prove whether the following is valid:

$\sin^{2}A + \cot^{2}A = \frac{2\sin^{4}A +2\cos^{2}A}{1 - \cos 2A}$

3

Simplify using the trigonometric power reducing formula.

4

Simplify the expression $\frac{\sin x}{1 + \cos x} + \frac{1 + \cos x}{\sin x}$ .

5

Which of the following is the simplified version of $\cot x \sec x \cos x \sin x$ ?

6

Use the power reducing formulas for trigonometric functions to reduce and simplify the following equation:

$\sin^{2}A \cos^{2} A$

7

Using trigonometric identities, determine whether the following is valid:

$\sin^{2} A \cos^{2} A = \frac{1-\cos^{4}A-2\cos^{2}A\sin^{2}A + \sin^{4}A}{4}$

8

Simplify the expression:

$\csc\theta(\sin\theta+\cos\theta \cot\theta)$

9

Simplify using identities:

$\frac{-\cos x+\sec x}{\tan x}$

10

Determine the value of: $(1+cot^2(\theta))(1-cos^2(\theta))$

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