Sinx.sin(60-x).sin(60+x)=1/4 (sin3x)
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Sinx.sin(60-x).sin(60+x)
= sinx [ cos( 60 - x - 60 - x) - cos ( 60 - x + 60+ x ) /2
= sinx [ cos ( -2x ) - cos ( 120 ) ] /2
= sinx [ cos2x + 1/2 ] /2
= sinx [ ( 1 - 2sin²x) + 1/2 ] /2
= sinx [ 3/2 - 2sin²x ] / 2
= 3 sinx/4 - 2 sin³x /2
= 3sinx - 4sin³x / 4
= 1/4 ( sin3x )
Hope helped!
Formulae : sin3x = 3sinx - 4sin³x
2sinA* sinB = cos (A - B) - cos ( A + B)
= sinx [ cos( 60 - x - 60 - x) - cos ( 60 - x + 60+ x ) /2
= sinx [ cos ( -2x ) - cos ( 120 ) ] /2
= sinx [ cos2x + 1/2 ] /2
= sinx [ ( 1 - 2sin²x) + 1/2 ] /2
= sinx [ 3/2 - 2sin²x ] / 2
= 3 sinx/4 - 2 sin³x /2
= 3sinx - 4sin³x / 4
= 1/4 ( sin3x )
Hope helped!
Formulae : sin3x = 3sinx - 4sin³x
2sinA* sinB = cos (A - B) - cos ( A + B)
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