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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. 32 (page 474)

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

Short Answer

Expert verified

We have proved the statement $(1 - \cos^{2} (胃)) (1 + \cot^{2} (胃)) = 1$ .

Step by step solution

01

Step 1. Given information.

We have:

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

02

Step 2. Establish the identity.

Take the left hand sides:

$(1 - \cos^{2} (胃)) (1 + \cot^{2} (胃))$

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

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

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

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

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Most popular questions from this chapter

Show that $\cos \frac{蟺}{8} = \frac{\sqrt{2 + \sqrt{2}}}{2}$ and use it to find $\sin \frac{蟺}{16}, \cos \frac{蟺}{16}$ .

In Problems 9鈥�36, find the exact value of each expression.

$\cot [\sin^{- 1} (- \frac{1}{2})]$

Find the value of the number C:

$\frac{1}{2} \sin^{2} x + C = - \frac{1}{4} \cos (2 x)$

solve each equation on the interval $0 鈮� 胃 < 2 蟺$

$\sin 胃 - \sqrt{3} \cos 胃 = 1$

In Problems 9鈥�36, find the exact value of each expression.

$\sec (\cos^{- 1} \frac{1}{2})$

See all solutions

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