Prove that the following identity is true.sin2tan xx sin x cos x=sin x - cos xcos x 2 cos xWe begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use theratio identity, and then factor the denominator. Finally we simplify by reducing the common factor.sin x(sin x + cos x)sin2 xsin x cos xCos X 1 -cos X 2 cos3 xcos x)sin x(sin x=sin2 xcos2 xCOS Xsin xcos xsin xsin2 x -COS Xsin x cos x= tan xsin2 xsin x cos x= tan x.(sin x - cos x)tan xsin x - cos x

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Asked Oct 20, 2019
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Prove that the following identity is true.
sin2
tan x
x sin x cos x
=
sin x - cos x
cos x 2 cos x
We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the
ratio identity, and then factor the denominator. Finally we simplify by reducing the common factor.
sin x(sin x + cos x)
sin2 xsin x cos x
Cos X 1 -
cos X 2 cos3 x
cos x)
sin x(sin x
=
sin2 xcos2 x
COS X
sin x
cos x
sin x
sin2 x -
COS X
sin x cos x
= tan x
sin2 x
sin x cos x
= tan x.
(sin x - cos x)
tan x
sin x - cos x
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Prove that the following identity is true. sin2 tan x x sin x cos x = sin x - cos x cos x 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simplify by reducing the common factor. sin x(sin x + cos x) sin2 xsin x cos x Cos X 1 - cos X 2 cos3 x cos x) sin x(sin x = sin2 xcos2 x COS X sin x cos x sin x sin2 x - COS X sin x cos x = tan x sin2 x sin x cos x = tan x. (sin x - cos x) tan x sin x - cos x

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Step 1

Given informa...

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sin2xsinxcosx tan x The given equation is sinx cosx-2 cosx -COS

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Trigonometric Ratios