Trigonometric EquationMedium
Question
The values of θ satisfying sin 7θ = sin 4θ - sin θ and 0 < θ < 
are -
are -Options
A.
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D.
Solution
sin 7θ = sin4θ - sin θ
sin 7θ + sin θ = sin4θ
2sin4θ cos3θ = sin4θ
or 2sin4θ cos3θ - sin4θ = 0
sin4θ (2cos3θ -1) = 0
⇒ sin4θ = 0 or 2cos3θ - 1 = 0
if sin4θ = 0 ⇒ 4θ = π ⇒ =
and if 2cos3θ = 1 ⇒ 3θ = θ =
= θ = 
sin 7θ + sin θ = sin4θ
2sin4θ cos3θ = sin4θ
or 2sin4θ cos3θ - sin4θ = 0
sin4θ (2cos3θ -1) = 0
⇒ sin4θ = 0 or 2cos3θ - 1 = 0
if sin4θ = 0 ⇒ 4θ = π ⇒ =
and if 2cos3θ = 1 ⇒ 3θ = θ =
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