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Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e

Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section8.2: Trigonometric Form For Complex Numbers
Problem 78PS
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Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e
Transcribed Image Text:Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e
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