Question

prove the identity sin4x=2sin2xcos2x

Answer 1

Ok so think of it this way: 
sin4x=sin2(2x), and lets say that 2x=a
By the double angle theorem, we know that sin2a=2sin(a)cos(a)
So substitute 2x for a, and there you go!

Answer 2

The prove of the identity sin4x = 2sin2xcos2x is shown.

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Some trigonometric identities are:

sin(A + B) = sinAcosB + cosAsinB

Given the identity:

sin(4x)

sin(4x) = sin(2x + 2x)

Applying trigonometry identity:

sin(2x + 2x) = sin2xcos2x + cos2xsin2x

sin(2x + 2x) = 2sin2xcos2x

sin(4x) = 2sin2xcos2x

The prove of the identity sin4x = 2sin2xcos2x is shown.

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