How would I show that Sin4x=4sinxcosxcos2x?

Question

Need assistance in breaking it down

Answer 1

Sin4x can be written as Sin2(2x) And We Know Sin2A = 2sinAcosA Sin2(2x) = 2sin2xcos2x Now sin2x can be written as sinxcosx =2(2sinxcosx)cos2x =4sinxcosxcos2x

Answer 2

Left hand side identity = sin4x

= sin2(2x)

From the double angle formulas sin(2a) = 2 sin(a) cos(a)

= 2 sin(2x) cos(2x)

= 2[2 sin(x) cos(x)] cos(2x)

= 4 sin(x) cos(x) cos(2x)

= Right hand side identity.