Question

Sin 12theta -sin4theta = 2 cos 8theta . Sin 4 theta​

Answer 1

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)