## anonymous one year ago does 1/2sin^2x= -1/4 cos(2x)

• This Question is Open
1. anonymous

Expand out both sides to see if that's true

2. anonymous

not sure if I know how to do that..

3. anonymous

cos(2x)=cos(x+x). now tell me how to expand the right hand side?

4. anonymous

2sin(x)^2=-cos(2x) cos(2X)=1-2sin^2x so.. 2sin(x)^2=2sin(x)^2-1 ?

5. anonymous

yeah, actually. you're done!

6. anonymous

so not equal... :(

7. anonymous

does

8. anonymous

yeah, you arrived at a contradiction and it can't be true.

9. anonymous

$\int\limits_{?}^{?} cosxsinx dx$ = which one?

10. anonymous

integral of cosx * sinx dx I got the 1/2 sin^2(x) but my answer key I have the other one

11. anonymous

|dw:1433648150311:dw|

12. anonymous

|dw:1433648346891:dw|

13. anonymous

anyone? am I doing my U-sub wrong?

14. anonymous

That's correct as far as I am concerned, the only thing missing is the Constant

15. anonymous

so then 1/2 sin^2x should = -1/4 cos(2x) ??

16. anonymous

In a question like this, aren't we proving that LHS = RHS, how did you resort to using integration?

17. anonymous

the question was the integration. What I got was the 1/2 sin^2 (x) and my prof answer key shows the -1/4 cos (2x) wondering who made the mistake of if they are the same

18. anonymous

|dw:1433649465541:dw|

19. anonymous

Well $$cos(2x) = 1-2sin^{2}x$$ So $$-\frac{1}{4}cos(2x) = -\frac{1}{4}(1-2sin^{2}x) =-\frac{1}{4} + \frac{1}{2}sin^{2}x$$ But keep in mind that we have that constant of integration, the +C. That plus C would absorb the -1/4 and leave us with simply $$\frac{1}{2}sin^{2}x + C$$ Your answer is equivalent as far as Im concerned.

20. anonymous

OK Thank you Concentrating!

21. anonymous

You're welcome :)