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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 36 (page 474)

In problems 19-98, establish each identity.
$\csc^{4} (胃) - \csc^{2} (胃) = \cot^{4} (胃) + \cot^{2} (胃)$

Short Answer

Expert verified

We have proved the identity $\csc^{4} (胃) - \csc^{2} (胃) = \cot^{4} (胃) + \cot^{2} (胃)$ .

Step by step solution

01

Step 1. Given information.

We have:

$\csc^{4} (胃) - \csc^{2} (胃) = \cot^{4} (胃) + \cot^{2} (胃)$

02

Step 2. Establish the identity.

Take the left hand sides:

$\csc^{4} (胃) - \csc^{2} (胃)$

Break:

$= \csc^{2} (胃) \csc^{2} (胃) - \csc^{2} (胃) = \csc^{2} (胃) (\csc^{2} (胃) - 1)$

Apply identity: $\csc^{2} (胃) - 1 = \cot^{2} (胃)$

$= (1 + \cot^{2} (胃)) \cot^{2} (胃) = \cot^{4} (胃) + \cot^{2} (胃)$

Hence, proved.

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Most popular questions from this chapter

find the exact value of the expression

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