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
Worksheet by Kuta Software LLC
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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
Worksheet by Kuta Software LLC
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sec x csc x
12)
=
1 - cos 2x sin 2x
Worksheet by Kuta Software LLC
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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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