Prove that the given equation is not an identity by finding a value of x for which the two sides have different values.csc x = V1- cot 2xChoose the correct value of x for which the two sides have different values.O A. x=4В. X32C. x=2Calculate the two sides at this value of x.CSC X =1- cotx =(Type exact answers, using radicals as needed.)

Given, Cosecx=1-cot2x Now squaring both sides,…

Answered: Prove that the given equation is not an…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Prove that the given equation is not an identity by finding a value of x for which the two sides have different values.
csc x = V1- cot 2x
Choose the correct value of x for which the two sides have different values.
O A. x=
4
В. X3
2
C. x=
2
Calculate the two sides at this value of x.
CSC X =
1- cotx =
(Type exact answers, using radicals as needed.)

Expert Solution

Step 1

Given, $C o s e c x = \sqrt{1 - c o t^{2} x}$

Now squaring both sides,

$C o s e c x = \sqrt{1 - c o t^{2} x} \cos e c^{2} x = 1 - c o t^{2} x \cos e c^{2} x + c o t^{2} x = 1 \frac{1}{\sin^{2} x} + \frac{\cos^{2} x}{\sin^{2} x} = 1 \frac{1 + \cos^{2} x}{\sin^{2} x} = 1 1 + \cos^{2} x = \sin^{2} x \cos^{2} x - \sin^{2} x = - 1 \cos 2 x = - 1 2 x = 2 n π \pm π x = nπ \pm π / 2 \forall n \in Z x = . . . . . . . π / 2, 3 π / 2, 5 π / 2, . . . . . . . so on$

Thus among the given options, for $π / 2 a n d 5 π / 2$ $C o s e c x = \sqrt{1 - c o t^{2} x}$ .

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