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The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity.
tan(x)sin(2x)
= tan(x)∙[2sin(x)cos(x)]
= StartFraction sine (x) Over cosine (x) EndFraction times 2 sine (x) cosine (x)
= 2sin2(x)
= 1 – cos(2x)
What are the correct justifications, listed in proper order?
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity
Double Angle Identity, Simplify, Double Angle Identity, Quotient Identity for Tangent
Double Angle Identity, Simplify, Quotient Identity for Tangent, Double Angle Identity
Double Angle Identity, Quotient Identity for Tangent, Double Angle Identity, Simplify

Respuesta :

Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity

The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity is option A

Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity.

What is double angle identity?

The sin2x formula is the double angle identity used for sine function in trigonometry. Trigonometry is a branch of mathematics where we study the relationship between the angles and sides of a right-angled triangle. The formula for sin2x: sin2x = 2 sin x cos x (in terms of sin and cos)

Given

1 – cos(2x) = tan(x)sin(2x)

Taking R.H.S

tanx.sin2x

= tanx(2 sinx cosx)

2 sinx cosx is a double angle identity

= [tex]\frac{sinx}{cosx} .(2 sinxcosx)[/tex]

[tex]\frac{sinx}{cosx}[/tex] is a quotient identity for tangent

= [tex]2sin^{2} x[/tex]

We have simplify by cancelling out cosx.

= 1 - cos(2x)

It is a double angle identity.

Find out more information about double angle identity here

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