Question

Use your knowledge of the half-angle and double-angle identities to simplify the following

(4sin(2a))-(2sin(2a))(4sin^2(a))

Answer 1

4 sin ( 2α ) - 2 sin ( 2α ) 4 sin² α =

4 sin ( 2α ) - 4 sin ( 2α ) ∙ 2 ∙ sin² α =

4 sin ( 2α ) ( 1 - 2 sin² α ) =
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Remark:

1 - 2 sin² α = cos ( 2α )
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4 sin ( 2α ) ∙ cos ( 2α ) =

2 ∙ [ 2 sin ( 2α ) ∙ cos ( 2α ) ] =

2 ∙ sin ( 2 ∙ 2α ) =

2 ∙ sin ( 4α )