Simplify the expression as much as possible. sin(2x)cos(x)
1 answer:
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))
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))
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