Double Angle Identity Practice - Weebly

[Pages:6]Accel. Precalculus

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Double Angle Identity Practice

Date________________ Period____

Verify each identity.

1) sin 4x ? (1 - cos 2x) = 2sin2 xtan 4x

cos 4x

2sin xcos x

2)

= tan 2x

cos 2x

3) csc2 x - 2cos2 x = cot2 x - cos 2x

Worksheet by Kuta Software LLC

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4) 2cos2 x + tan2 x = sec2 x + cos 2x

sin 2x 5) 2sin xcos xcot x =

tan x

6) 2sin xcos2 x = 1 + cos 2x csc x

sin2 x + cos 2x cot x

7)

=

sin2 x

tan x

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tan2 x

1

8)

=

2sin2 x 1 + cos 2x

1

cos2 x

9)

=

1 - tan2 x cos 2x

sin 2x 2

10)

=

sin2 x tan x

11) -2sin xcos xtan x = cos 2x - 1

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sec x csc x

12)

=

1 - cos 2x sin 2x

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Answers to Double Angle Identity Practice

sin 4x ? (1 - cos 2x)

1)

cos 4x

Use cos 2x = 1 - 2sin2 x

2sin xcos x 2) cos 2x

Use sin 2x = 2sin xcos x

2sin 4xsin2 x cos 4x

sin 4x Use tan 4x =

cos 4x

sin 2x cos 2x

sin 2x Use tan 2x =

cos 2x

2sin2 xtan 4x 3) csc2 x - 2cos2 x

Use cot2 x + 1 = csc2 x

cot2 x + 1 - 2cos2 x Use cos 2x = 2cos2 x - 1

tan 2x

4) 2cos2 x + tan2 x

Use cos 2x = 2cos2 x - 1

tan2 x + 1 + cos 2x Use tan2 x + 1 = sec2 x

cot2 x - cos 2x 5) 2sin xcos xcot x

Use sin 2x = 2sin xcos x

cot xsin 2x

1 Use cot x =

tan x

sec2 x + cos 2x 6) 2sin xcos2 x

Use cos 2x = 2cos2 x - 1

sin x ? (1 + cos 2x)

1 Use csc x =

sin x

sin 2x

tan x

sin2 x + cos 2x

7)

sin2 x

Use cos 2x = cos2 x - sin2 x

1 + cos 2x

csc x tan2 x 8) 2sin2 x

Decompose into sine and cosine

cos2 x sin2 x

cot2 x

cot x tan x

1 9) 1 - tan2 x

cos x Use cot x =

sin x 1

Use cot x = tan x

Decompose into sine and cosine

( )sin x 2

cos x 2sin2 x

Simplify

1 2cos2 x

Use cos 2x = 2cos2 x - 1

1

1 + cos 2x sin 2x 10) sin2 x

Use sin 2x = 2sin xcos x

1

( )sin x 2

1 cos x

Simplify

2sin xcos x sin2 x

Cancel common factors

cos2 x cos2 x - sin2 x

Use cos 2x = cos2 x - sin2 x

2cos x sin x

sin x Use tan x =

cos x

2

cos2 x

tan x

cos 2x

Worksheet by Kuta Software LLC

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sin x

11) -2sin xcos xtan x

Use tan x = cos x

2sin2 xcos x -

cos x

Cancel common factors

-2sin2 x

Use cos 2x = 1 - 2sin2 x

cos 2x - 1

sec x 12) 1 - cos 2x

Use cos 2x = 1 - 2sin2 x

sec x 2sin2 x

1 Use sec x =

cos x

1 2cos xsin2 x

Use sin 2x = 2sin xcos x

1 sin 2xsin x

1 Use csc x =

sin x

csc x

sin 2x

Worksheet by Kuta Software LLC

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