Question

Derive: sin2x=2sinxcosx

Answer 1

You can take the derivative of either side (though the lefthand side will be easier).

Answer 2

sin(2x)=sin(x+x)
=sinxcosx+cosxsinx FORMULA :(sin(A+B)=sinAcosB+cosAsinB)
=2sinxcosx

Answer 3

considering how the derivative of sinx is cosx i believe that with assumption that \[\lim_{x \rightarrow 2x}\] ( it is valid ) the derivative of sin2x will be cos2x which is equal to \[1-2 \sin ^{2} x\] This is however simply my assumption