Prove the following identity3 sin e - 4 sin3 esin 30We 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 termswith double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines.+e)sin 30= sin(am(cos e)(cos 20)(sin 0)sin(cos e) (1 - 2 sin2 e)(sin e)2 sin 0sin 0 2 sin3 e= 2 sin esin 0 2 sin3 e= (2 sin e)1 -sin 0 2 sin3 e= 2 sin e -= 3 sin 0 - 4 sin3 e

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Asked Oct 20, 2019
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Prove the following identity
3 sin e - 4 sin3 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.
+e)
sin 30= sin
(am
(cos e)
(cos 20)(sin 0)
sin
(cos e) (1 - 2 sin2 e)(sin e)
2 sin 0
sin 0 2 sin3 e
= 2 sin e
sin 0 2 sin3 e
= (2 sin e)1 -
sin 0 2 sin3 e
= 2 sin e -
= 3 sin 0 - 4 sin3 e
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Prove the following identity 3 sin e - 4 sin3 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. +e) sin 30= sin (am (cos e) (cos 20)(sin 0) sin (cos e) (1 - 2 sin2 e)(sin e) 2 sin 0 sin 0 2 sin3 e = 2 sin e sin 0 2 sin3 e = (2 sin e)1 - sin 0 2 sin3 e = 2 sin e - = 3 sin 0 - 4 sin3 e

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Expert Answer

Step 1

To prove:

sin 30 3sine - 4 sin3 0
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sin 30 3sine - 4 sin3 0

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Step 2

Note:

...
The formula that will be used are as follows:
sin 2x 2 sin x cos x
cos 2x 1 2 sin2 :
sin2 xcos2 x = 1
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The formula that will be used are as follows: sin 2x 2 sin x cos x cos 2x 1 2 sin2 : sin2 xcos2 x = 1

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Math

Trigonometry

Trigonometric Ratios