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2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

Calculus: Early Transcendentals
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 the given identity. 2 In sin 2x - 2 In (1 + cos 2x) = 2 In tan x Rewrite the left side as a single logarithm using only the properties of logarithms. 2 In sin 2x - 2 In (1 + cos 2x) = In (Do not simplify.) Now rewrite the numerator and denominator so that they have arguments of x for all the trigonometric function: The simplest numerator is obtained using The simplest denominator is obtained using Apply these two identities to the numerator and denominator of the last expression. 2 In sin 2x - 2 In (1 + cos 2x) = In (Do not simplify.) Then simplify the argument of the logarithm. 2 In sin 2x - 2 In (1 + cos 2x) = In The identity can be used to rewrite the argument using a single trigonometric function. Apply this identity to the argument. 2 2 In sin 2x - 2 In (1 + cos 2x) = In Finally, using changes the expression to be exactly equal to 2 In tan x.
Transcribed Image Text:Prove the given identity. 2 In sin 2x - 2 In (1 + cos 2x) = 2 In tan x Rewrite the left side as a single logarithm using only the properties of logarithms. 2 In sin 2x - 2 In (1 + cos 2x) = In (Do not simplify.) Now rewrite the numerator and denominator so that they have arguments of x for all the trigonometric function: The simplest numerator is obtained using The simplest denominator is obtained using Apply these two identities to the numerator and denominator of the last expression. 2 In sin 2x - 2 In (1 + cos 2x) = In (Do not simplify.) Then simplify the argument of the logarithm. 2 In sin 2x - 2 In (1 + cos 2x) = In The identity can be used to rewrite the argument using a single trigonometric function. Apply this identity to the argument. 2 2 In sin 2x - 2 In (1 + cos 2x) = In Finally, using changes the expression to be exactly equal to 2 In tan x.
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