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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. 45 (page 474)

In problems 19-98, establish each identity.
$\frac{\sec (胃)}{\csc (胃)} + \frac{\sin (胃)}{\cos (胃)} = 2 \tan (胃)$

Short Answer

Expert verified

We have proved the identity $\frac{\sec (胃)}{\csc (胃)} + \frac{\sin (胃)}{\cos (胃)} = 2 \tan (胃)$ .

Step by step solution

01

Step 1. Given information.

We have:

$\frac{\sec (胃)}{\csc (胃)} + \frac{\sin (胃)}{\cos (胃)} = 2 \tan (胃)$

02

Step 2. Establish the identity.

Take the left hand side:

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

Apply identity: $s e c 胃 = \frac{1}{\cos 胃}, c s c 胃 = \frac{1}{\sin 胃}$

role="math" localid="1646758300440" $= \frac{\frac{1}{\cos 胃}}{\frac{1}{\sin 胃}} + \frac{\sin (胃)}{\cos (胃)} = \frac{1}{\cos 胃} 脳 \frac{\sin 胃}{1} + \frac{\sin (胃)}{\cos (胃)} = \frac{\sin 胃}{\cos 胃} + \frac{\sin (胃)}{\cos (胃)} = \tan 胃 + \tan 胃 = 2 \tan 胃$

Hence, proved.

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Most popular questions from this chapter

True or False: $\sin (- 胃) + \sin (胃) = 0$ for any value of theta

$\cos (- 胃) - \cos (胃)$

Establish each identity.

$\frac{1 + \sin 胃 + \cos 胃}{1 + \sin 胃 - \cos 胃} = \frac{1 + \cos 胃}{\sin 胃}$

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

$\sec (\tan^{- 1} \sqrt{3})$

Show that $\cos (\sin^{- 1} (v) + \cos^{- 1} (v)) = 0$

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