Find the general solution of the following equation:
$sin 9 θ = sin θ$

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Solution

$sin 9 θ = sin θ (Given)$
$sin 9 θ - sin θ = 0$
$2 cos (\frac{9 θ + θ}{2}) sin (\frac{9 θ - θ}{2}) = 0$
$\Rightarrow cos 5 θ \cdot sin 4 θ = 0$
$\Rightarrow cos 5 θ = 0$ OR $sin 4 θ = 0$
$\Rightarrow 5 θ = (n + \frac{1}{2}) π$ OR $4 θ = n π$
$\Rightarrow θ = \frac{(2 n + 1) π}{10}$ OR $θ = \frac{n π}{4}$

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