Find the general solution of sin 9θ = sin θ.

1.	Find the general solution of sin 9θ = sin θ.
Answer» sin 9θ = sin θ ⇒ 9θ = 2nπ + θ or 9θ = (2n + 1) π - θ, n∈I (∵ sin θ = sin α ⇒ θ = nπ + (–1)ⁿ α, where n∈I) ⇒ θ = \(\frac{2n\pi}{8}\) or θ = \(\frac{(2n+1)\pi}{10}\) ⇒ θ = \(\frac{n\pi}{4}\) or \(\frac{(2n+1)\pi}{10}\)

Answer»

sin 9θ = sin θ

⇒ 9θ = 2nπ + θ or 9θ = (2n + 1) π - θ, n∈I (∵ sin θ = sin α ⇒ θ = nπ + (–1)ⁿ α, where n∈I)

⇒ θ = \(\frac{2n\pi}{8}\) or θ = \(\frac{(2n+1)\pi}{10}\)

⇒ θ = \(\frac{n\pi}{4}\) or \(\frac{(2n+1)\pi}{10}\)

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