4sina sin(60-a) sin(60+a)= sin3a
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Answered by
95
Given 4 sin a sin(60-a) sin(60 + a) can be written as
4 sin a ((sin 60 - a) + sin (60 - a))
4 sin a(sin^2 60 - sin^2 a)
4 sin a((root 3/2)^2 - sin ^2 a)
4 sin a(3/4 - sin^2 a)
4 ( 3 sin a - 4 sin^3 a/4)
4(1/4(sin 3a)
sin 3a.
4 sin a ((sin 60 - a) + sin (60 - a))
4 sin a(sin^2 60 - sin^2 a)
4 sin a((root 3/2)^2 - sin ^2 a)
4 sin a(3/4 - sin^2 a)
4 ( 3 sin a - 4 sin^3 a/4)
4(1/4(sin 3a)
sin 3a.
Answered by
73
4 sin a sin (60- a) sin (60 + a )
As Sin ( a- b ) sin ( a+b ) = sin²a - sin² b
4 Sin a * [ Sin² 60 - Sin² a ]
4 Sin a * [ 3/4 - Sin ² a ]
3 Sin a - 4 Sin ³ a = Sin 3a
As Sin ( a- b ) sin ( a+b ) = sin²a - sin² b
4 Sin a * [ Sin² 60 - Sin² a ]
4 Sin a * [ 3/4 - Sin ² a ]
3 Sin a - 4 Sin ³ a = Sin 3a
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