Chapter 5: Q 3. (page 495)

Use Pythagorean identities to rewrite each of the following trigonometric expressions.
$\tan^{2} x =_______$

Short Answer

Expert verified

The obtained result is $\frac{1}{\cos^{2} x} - 1$ .

Step by step solution

Step 1. Given information.

Consider the given expression.

$\tan^{2} x$

Step 2. Apply the Pythagorean identities to rewrite the expression.

The Pythagorean identity is defined as,

$\sin^{2} x + \cos^{2} x = 1$

Use the identity to write the given expression.

$\begin{array}{rcl} \sin^{2} x + \cos^{2} x & = & 1 \\ \sin^{2} x & = & 1 - \cos^{2} x \\ \frac{\sin^{2} x}{\cos^{2} x} & = & \frac{1 - \cos^{2} x}{\cos^{2} x} \\ \tan^{2} x & = & \frac{1}{\cos^{2} x} - \frac{\cos^{2} x}{\cos^{2} x} \\ = & \frac{1}{\cos^{2} x} - 1 \end{array}$

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Use Pythagorean identities to rewrite each of the following trigonometric expressions.
$\tan^{2} x =_______$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the Pythagorean identities to rewrite the expression.

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Use Pythagorean identities to rewrite each of the following trigonometric expressions.tan2x=_______

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the Pythagorean identities to rewrite the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Statistics

Pure Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Use Pythagorean identities to rewrite each of the following trigonometric expressions.
$\tan^{2} x =_______$