Prove that: `\ sin3A+sin2A-sin A=4sin A cos A/2cos3A/2`

Explanation

We have to proof,

`sin(3A^o)+sin(2A^o)-sin(A^o)=4sin A cos A/2cos3A/2`

Let,

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

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(((3A^o)+(2A^o))/2)cos(((3A^o)+(2A^o))/2)-sin(A^o)`

L.H.S.=`2sin((5/2)A^o)cos((1/2)A^o)-sin(A^o)`

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