## anonymous one year ago If Sin(x)+Cos(x)=5/4, What is Sin(2x) given that 0<x<pi/2

1. dan815

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2. anonymous

So Tan x=5/4? If so, Im confused on what to do next

3. dan815

sry wait

4. dan815

5. dan815

sin(2x)= 2sin(x) cos(x) this is an identity

6. dan815

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7. dan815

now solve for x

8. anonymous

Sorry to be a bother, but how'd you get it to match the identity like that?

9. dan815

i multiplied both sides by 2cosx

10. dan815

since that would make the left side equal to sin(2x)

11. dan815

now u end up with nice working equations

12. dan815

by divide both sides by cos(x)

13. dan815

ugh lemme think what can we do with this now

14. dan815

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15. dan815

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16. dan815

you gotta solve these 2 system of equations somehow

17. anonymous

Since the problem only asks for What Sin2x equals, wouldn't -2Cos^2(x)+5/2Cos(x) be correct?

18. dan815

well i guess, but are u sure they arent looking for value for x

19. anonymous

I just checked. They only want Sin2x=... Thank you so much

20. dan815

ok you're welcome!