Simplify the expression as much as possible:

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

For this kind of exercise you need to know the trigonometric identities. In this case: --->sin(2a)=2(sen(a)*cos(a)) (That comes from sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b), since 2a is just a sum a a+a) --->sin^2(a)+cos^2(a)=1 That way you can start transforming things and simplifying. By doing that I got to: 2sin(x)*cos^2(x) (or 2sin(x)-2sin^3(x)) I attached the steps I followed as an image (I made a mistake on paper at the very end, that's a multiplication not a substraction, it's 2sin(x)*cos^2(x))

Answered by ljndr | 2024-06-10

The expression sin ( 2 x ) cos ( x ) simplifies to 2 sin ( x ) cos 2 ( x ) using the double angle identity for sine. We substitute and expand the terms. This gives a clean, simplified result of the expression.
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Answered by ljndr | 2024-11-24