Prove the following identity.(sin x - cos x) = 1 - sin 2xWe begin by expanding the left side of the equation, and then regroup. We can then use a Pythagorean Identity and a Double-Angle Formula to simplify.sinx2 sin x cos x +(sin x cos x)2 :(sin2-2 sin x cos x=- 2 sin x COs X= 1 - sin 2x

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Asked Oct 20, 2019
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Prove the following identity.
(sin x - cos x) = 1 - sin 2x
We begin by expanding the left side of the equation, and then regroup. We can then use a Pythagorean Identity and a Double-Angle Formula to simplify.
sinx2 sin x cos x +
(sin x cos x)2 :
(sin2
-2 sin x cos x
=
- 2 sin x COs X
= 1 - sin 2x
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Prove the following identity. (sin x - cos x) = 1 - sin 2x We begin by expanding the left side of the equation, and then regroup. We can then use a Pythagorean Identity and a Double-Angle Formula to simplify. sinx2 sin x cos x + (sin x cos x)2 : (sin2 -2 sin x cos x = - 2 sin x COs X = 1 - sin 2x

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Expert Answer

Step 1

Use (a-b)^2= a^2 -2ab+ b^2 formula to expand i...

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(sin x - cos x) =sinx +2sinx cosx+cos'x

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Trigonometry