sin 7x = sin 3x⇒sin 7x - sin 3x = 0⇒2 cos 7x+3x2 sin7x-3x2 = 0⇒2 cos 5x sin 2x = 0⇒cos 5x = 0 or sin 2x = 0⇒ 5x =2m+1π2 or 2x = nπ⇒x =2m+1π10 or x = nπ2; where m,n∈I

sin 7x = sin 3x

\sin 7 x = \sin 3 x \Rightarrow \sin 7 x - \sin 3 x = 0 \Rightarrow 2 \cos (\frac{7 x + 3 x}{2}) \sin (\frac{7 x - 3 x}{2}) = 0 \Rightarrow 2 \cos 5 x . \sin 2 x = 0 \Rightarrow \cos 5 x = 0 or \sin 2 x = 0 \Rightarrow 5 x = (2 m + 1) \frac{π}{2} or 2 x = nπ \Rightarrow x = (2 m + 1) \frac{π}{10} or x = \frac{nπ}{2}; where m, n \in I

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