SOLUTION: Simplify the given expression. sin(2x) cos(4x) − sin(4x) cos(2x)

Question 1204009: Simplify the given expression.
sin(2x) cos(4x) − sin(4x) cos(2x)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

use identities

then we have

=
=
=
=
=
=

Reduced trigonometric form:
=

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

In this problem, they expect that you will use this standard Trigonometry identity

            sin(a)*cos(b) - cos(a)*sin(b) = sin(a+b),

which is valid for any/all angles " a " and " b ".

Then the solution is in one line, as it is shown below.

Let a = 2x, b= 4x. Then sin(2x)*cos(4x) − sin(4x)*cos(2x) = sin(2x-4x) = sin(-2x) = -sin(2x).

Solved and completed.

=============================

The method shown in my post, is a traditional
and standard method solving similar problems.

If you will solve it as @MathLover1 does, your teacher will learn
that you do not know a standard way solving such problems.

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