Sin4x = 2sin(2x).cos(2x)
= 4sinx.cosx.(2cos2x - 1)
= 8sinx.cos3x - 4sinx.cosx
Sin24x = 16sin2x.cos2x(4cos4x - 4cos2x - 1)
2Sin4x = 8sinx.cosx(2cos2x - 1)
L.H.S = sin24x + cos2x
= 64sin2x.cos6x - 64sin2x.cos4x - 16sin2x.cos2x
= 16sin2x.cos2x( 4cos4x - 4cos2x - 1)
R.H.S = 2sin4x.cos4x
= 8sinx.cosx(2cos2x - 1) * cos4x
= 8sinx.cos5x(2cos2x - 1)
= 16sinx.cos7x - 8sinx.cos5x
= 8sinx.cos5x( 2cos2x - 1)
therefore,
16sin2x.cos2x( 4cos4x - 4cos2x - 1) = 8sinx.cos5x( 2cos2x - 1)
16sin2x.cos2x( 2cos2x - 1)2 = 8sinx.cos5x( 2cos2x - 1)
16sin2x.cos2x( 2cos2x - 1) = 8sinx.cos5x
2sinx( 2cos2x - 1) = cos3x
4sinx.cos2x - 2sinx = cos3x
solve further and you'll get the answer.
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Moderation Team
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