Prove that: `(sin5x+sin3x)/(cos5x+cos3x)=t a n4x`

Explanation

`LHS`



`frac{2 Sin frac{5 x+3 x}{2} Cos frac{5 x-3 x}{2}}{2 Cos frac{5 x+3 x}{2} Cos frac{5 x-3 x}{2}}`


`Rightarrow frac{Sin 4 x Cos x}{Cos 4 x Cos x }`


`Rightarrow tan 4 x`




`= RHS`