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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. 31 (page 474)

In problems 19-98, establish each identity.
$\cos^{2} (胃) (1 + \tan^{2} (胃)) = 1$

Short Answer

Expert verified

We have proved the identity $\cos^{2} (胃) (1 + \tan^{2} (胃)) = 1$ .

Step by step solution

01

Step 1. Given information.

We have:

$\cos^{2} (胃) (1 + \tan^{2} (胃)) = 1$

02

Step 2. Establish the identity.

Take the left side:

$\cos^{2} (胃) (1 + \tan^{2} (胃))$

Apply identity: $\tan 胃 = \frac{\sin 胃}{\cos 胃}$

$\cos^{2} (胃) (1 + \frac{\sin^{2} (胃)}{\cos^{2} (胃)}) = \cos^{2} (胃) + \frac{\cos^{2} (胃) \sin^{2} (胃)}{\cos^{2} (胃)} = \cos^{2} (胃) + \sin^{2} (胃)$

Apply identity: localid="1646509068283" $\cos^{2} 胃 + \sin^{2} 胃 = 1$

$= 1$

Hence, identity proved.

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Most popular questions from this chapter

Rewrite over a common denominator:

$\frac{\sin (胃) + \cos (胃)}{\cos (胃)} + \frac{\sin (胃) + \cos (胃)}{\sin (胃)}$

Repeat Problem $107$ for $g (x) = \cos^{2} x$ .

$掳$ find the exact value of the expression

sin255 $掳$ -sin15 $掳$

find the exact value of the expression

sin 75 $掳$ + sin 15 $掳$

Establish each identity.

${(2 a \sin 胃 \cos 胃)}^{2} + a^{2} {(\cos^{2} 胃 - \sin^{2} 胃)}^{2} = a^{2}$

See all solutions

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