`(sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)`

Explanation

We have to proof,

`(sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)`

Let,

L.H.S=`(sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)`

As we know the formula,
`sin(A^o)+sin(B^o)= 2sin(((A^o)+(B^o))/2)cos(((A^o)-(B^o))/2)`

then,

L.H.S.=`(2sin(((5A^o)+(A^o))/2)cos(((5A^o)-(A^o))/2)+2sin(3A^o))/(2sin(((7A^o)+(3A^o))/2)cos(((7A^o)-(3A^o))/2)+2sin(5A^o))`


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