Verify that the equaiton is an identity sin2x 2sin x cos x

Verify that the equaiton is an identity.

sin2x= 2sin x cos x , substitue 2x=x + x and apply the sine of a sum identity ( sin A+B) = sinAcosB+ cosAsinB

so,

sin2x=sin (x+x)

= ???

Solution

sin2x

=sin(x+x)

( sin A+B) = sinAcosB+ cosAsinB

=sinxcosx +cosxsinx

=sinxcosx+sinxcosx

=2sinxcosx

so sin2x=2sinxcosx is an identity