Explanation Given: The identity sin θ 2 = 1 − cos θ 2 The given identity can be derived by using the identities listed below. Basic trigonometric identities : Pythagorean identity sin 2 x + cos 2 x = 1 Complementary angles 1. sin ( π 2 − x ) = cos x 2. cos ( π 2 − x ) = sin x Addition formulas 1. sin ( x + y ) = sin x cos y + cos x sin y 2. cos ( x + y ) = cos x cos y − sin x sin y Double-angle formulas 1. sin 2 x = 1 2 ( 1 − cos 2 x ) 2. cos 2 x = 1 2 ( 1 + cos 2 x ) 3. cos 2 x = cos 2 x − sin 2 x 4. sin 2 x = 2 sin x cos x Shift formulas 1. sin ( x + π 2 ) = cos x 2. cos ( x + π 2 ) = − sin x In the double angle formula 1, we have sin 2 x = 1 2 ( 1 − cos 2 x )

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 1.4, Problem 49E

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The derivation of the identity sinθ2=1−cosθ2

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Chapter 1.4, Problem 48E

Chapter 1.4, Problem 50E

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CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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The derivation of the identity sin θ 2 = 1 − cos θ 2

Solution Summary: The author explains how the identity mathrmsintheta is derived by using the basic trigonometric identities listed below.

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The derivation of the identity sinθ2=1−cosθ2

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