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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. 13 (page 505)

Establish the identity
$\tan 胃 + c o t 胃 = 2 c s c (2 胃)$

Short Answer

Expert verified

By converting tan $胃$ and cot $胃$ into sin $胃$ and cos $胃$

we get the tan $胃$ + cot $胃$ =2csc(2 $胃$ )

Step by step solution

01

Step 1. Given information

$\tan 胃 + c o t 胃 = 2 c s c (2 胃)$

02

Step 2. Calculations

$\tan 胃 + c o t 胃 = 2 c s c (2 胃) T a k e L H S, \tan 胃 + c o t 胃 \frac{\sin 胃}{\cos 胃} + \frac{\cos 胃}{\sin 胃} = \frac{\sin^{2} 胃 + \cos^{2} 胃}{\cos 胃 \sin 胃} \tan 胃 = \frac{\sin 胃}{\cos 胃} c o t 胃 = \frac{\cos 胃}{\sin 胃} = \frac{1}{\cos 胃 \sin 胃} = \frac{2}{2 \cos 胃 \sin 胃} = \frac{2}{\sin 2 胃} 2 \cos 胃 \sin 胃 = \sin 2 胃 = 2 c s c (2 胃)$

Hence LHS=RHS

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Most popular questions from this chapter

True or False: $\sin (- 胃) + \cos (- 胃) = \cos (胃) - \sin (胃)$

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

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

$\cos [\sin^{- 1} (- \frac{\sqrt{3}}{2})]$

Establish each identity.

$\tan 胃 + c o t 胃 = s e c 胃 c s c 胃$

solve each equation on the interval

$0 鈮� 胃鈮� 2 蟺$

$\sin 胃 - \cos 胃 = - \sqrt{2}$

See all solutions

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