Solve the problem. sin2x - sin4x

Macioccujx 2022-07-30 Answered
Solve the problem.
sin 2 x sin 4 x
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Answers (2)

minotaurafe
Answered 2022-07-31 Author has 22 answers
sin 2 x sin 4 x = sin 2 x 2 sin 2 x . cos 2 x = sin 2 x ( 1 2 cos 2 x )
= sin 2 x ( 1 cos 2 x + 1 ) = 2 sin x cos x ( 1 2 cos 2 x )
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Ismael Molina
Answered 2022-08-01 Author has 2 answers
sin ( α + β ) = sin α cos β + cos α sin β
sin ( α β ) = sin α cos β cos α sin β
sin ( α + β ) sin ( α β ) = 2 cos α sin β , assume α + β = p and α β = q
α + β = p
α β = q + 2 α = p + q => α = 1 / 2 ( p + q )
α + β = p
α β = q 2 β = p q => β = 1 / 2 ( p q )
sin p sin q = 2 cos 1 / 2 ( p + q ) sin 1 / 2 ( p q )
sin 2 x sin 4 x = 2 cos 1 / 2 ( 2 x + 4 x ) sin 1 / 2 ( 2 x 4 x )
= 2 cos 1 / 2 ( 6 x ) sin 1 / 2 ( 2 x )
= 2 cos 3 x sin x => sin ( x ) = sin x
= 2 cos 3 x sin x
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