Sin 12theta -sin4theta = 2 cos 8theta . Sin 4 theta
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Given to prove that :-
sin12θ - sin4θ = 2cos8θ . sin4θ
PROOF :-
It is in form of sinC - sinD that is
sinC - sinD = 2cos (C+ D/2) sin (C-D/2)
So, by using this formula we can solve
sin12θ- sin4θ = 2cos(12θ+ 4θ/2) × sin(12θ-4θ/2)
sin12θ- sin4θ = 2cos(16θ/2) × sin (8θ/2)
sin12θ- sin4θ = 2cos8θ × sin4θ
Hence proved !
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Know more formulae :-
sinC + sinD = 2sin(C+D/2) cos(C-D/2)
sinC - sinD = 2cos (C+ D/2) sin (C-D/2)
cosC + cosD = 2cos(C+D/2) cos(C-D/2)
cosC - cosD = -2 sin(C+D/2) sin(C-D/2)
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