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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. 40 (page 474)

In problems 19-98, establish each identity.
$9 \sec^{2} (胃) - 5 \tan^{2} (胃) = 5 + 4 \sec^{2} (胃)$

Short Answer

Expert verified

We have proved the identity $9 \sec^{2} (胃) - 5 \tan^{2} (胃) = 5 + 4 \sec^{2} (胃)$ .

Step by step solution

01

Step 1. Given information.

We have:

$9 \sec^{2} (胃) - 5 \tan^{2} (胃) = 5 + 4 \sec^{2} (胃)$

02

Step 2. Establish the identity.

Take the left hand side:

$9 \sec^{2} (胃) - 5 \tan^{2} (胃)$

Apply identity: role="math" localid="1646583478228" $\tan^{2} 胃 = \sec^{2} (胃) - 1$
$= 9 \sec^{2} (胃) - 5 (s e c^{2} 胃 - 1) = 9 \sec^{2} (胃) - 5 s e c^{2} 胃 + 5 = 5 + 4 s e c^{2} (胃)$

Hence, proved.

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