Answer:
[tex]\frac{1}{2} [sin(4x)-sin(2x)][/tex]
Step-by-step explanation:
Use the Product-Sum identity to turn cos(3x) sin x into a sum.
Formula: cos(u) + sin(v) = [tex]\frac{1}{2}[sin(u+v)-sin(u-v)][/tex]
Plug 4x and 2x for u and v into the formula: [tex]\frac{1}{2}[sin(3x+x)-sin(3x-x)][/tex]
Simplify: [tex]\frac{1}{2}[sin(4x)-sin(2x)][/tex]
:)
The expression is equivalent to cos(3x) sin x will be 1/2 [sin (4x ) - sin (2x)].
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
Formula we will use;
cos(u) + sin(v) = 1/2 [sin (u +v ) - sin (u - v)]
Now, Plug 4x and 2x for u and v into the formula:
1/2 [sin (3x + x ) - sin (3x - x)]
Simplify:
1/2 [sin (4x ) - sin (2x)]
Learn more about expression here;
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