Verified answer

We know that

Sin(A+B)=sinA cosB +cosA sinB

Now,putting B=A in the above formula,we get

sin(A+A)=sinA cosA+cosA sinA

or,sin 2A=2 sinA cosA (Proved

Yes, and cos2A = cos^2 A - sin^2 A

sin2A= 2sinA*cosA

= sin 2A

= sin ( A + A )

= sinAcosA + cosAsinA

= 2sinA cosA =

sin (A + A) = sin A + cos A

sin (A + A) = sin A + sin A. cos A

sin 2A = A

sin 2A

=sin (A+A)

=sin A cos A+ cos A sin A

=2sinAcosA

yes

yup