i am trying to reduce this further… what do i do..
y^'= 2 sinx(cos(x)sin(2x)+sin(x)cos(2x))

Question

i am trying to reduce this further… what do i do..
y^'= 2 sinx(cos(x)sin(2x)+sin(x)cos(2x))

anonymous · Answer

$$y \prime= 2sinx(cosxsin2x+sinxcos2x)$$

btaylor · Answer

The part with cos(x)sin(2x)+sin(x)cos(2x) looks like the angle addition identity for sine:
$$\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)$$
So, you can simplify that chunk to sin(x+2x), or sin(3x).

anonymous · Answer

my final answer should be $$2\sin^2(x)(2\cos(2x)+1)$$

btaylor · Answer

where do you get the sin^2?

btaylor · Answer

I'd get: $$2 \sin (x) \sin(3x)$$

anonymous · Answer

no idea. he gives us answers to the problem but we have to show steps and that is answer he has given

btaylor · Answer

I'm not sure how to get there...sorry!

anonymous · Answer

thanks anyways! i don't think he uses identities.