Question

prove sin 2x is equal to 2 sin x cos x​

Answer 1

we know,

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.