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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. 39 (page 474)

In problems 19-98, establish each identity.
$3 \sin^{2} (胃) + 4 \cos^{2} (胃) = 3 + \cos^{2} (胃)$

Short Answer

Expert verified

We have proved the identity $3 \sin^{2} (胃) + 4 \cos^{2} (胃) = 3 + \cos^{2} (胃)$ .

Step by step solution

01

Step 1. Given information.

We have:

$3 \sin^{2} (胃) + 4 \cos^{2} (胃) = 3 + \cos^{2} (胃)$

02

Step 2. Establish the identity.

Take the left hand side:

$3 \sin^{2} (胃) + 4 \cos^{2} (胃)$

Apply identity: $\sin^{2} (胃) = 1 - \cos^{2} 胃$

$= 3 (1 - \cos^{2} (胃)) + 4 \cos^{2} (胃) = 3 - 3 \cos^{2} 胃 + 4 \cos^{2} (胃) = 3 + \cos^{2} (胃)$

Hence, proved.

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