Prove that `cot4x(sin5x+sin3x)=cot x(sin5x-sin3x)`

Explanation

`cot 4 x(sin 5 x+sin 3 x)=cot x(sin 5 x-sin 3 x)`


`{LHS}`



`cot 4 x[2 sin (frac{5 x+3 x}{2}) cos (frac{5 x-3 x}{2})] `


`Rightarrow cot 4 x[2 sin 4 x cos x] `


`Rightarrow 2 frac{cos 4 x}{sin 4 x} x sin 4 x cdot cos x `


`Rightarrow 2 cos 4 x cos x`



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