Question

Prove

sinx=2sin(1/2)xcos(1/2)x

Answer 1

sin(2x)=2sinxcosx, you can change the argument(the thing in parentheses) and obtain the answers

Answer 2

its simple, If u angle on the left hand side is 2x then obviously the angle should be x, Because remember that the angle on the right hand side always half of the left hand side.
so If I say sin8x, then it must be equal to sin8x=2sin4xcos4x
And U can prove it by sin(a+b) law, by placing b=a or a=b. so U will get the results