Question

Explain how is sin2x =2sinxcosx

Answer 1

we know,
one important identity ,
sin( A + B) =sinA.cosB + cosA. sinB

let A = x
B = x

then,
sin( x + x ) = sinx.cosx + cosx .sinx
sin2x = 2sinx.cosx


verify :-
Let x = 30°

LHS = sin60° = √3/2

RHS = 2sin30°.cos30° = 2× 1/2 × √3/2 =√3/2

LHS = RHS

this is true for all real value of x then ,
sin2x = 2sinx.cosx is also an identity.

Answer 2

Identity for solving this:

sin(A+B) = sinAcosB + cosAsinB

Let A and B be x respectively.

Then, 

Sin(2x) = Sin(x+x)
Sin(x+x) = Sin(x)Cos(x) + Cos(x)Sin(x)
Sin(2x) = 2Sin(x)Cos(x)