## order 3 years ago cosec x= 1/2 (x)+1 has root 0<x<1/2 pi verify by calculation that this root lies between 0.5 and 1

1. shivam_bhalla

Remember -1 <= sin x <= 1 Therefore -1 <= cosec x <=1 Now try :)

2. order

Still not sure..

3. shivam_bhalla

One more question. This is your question , right $cosec x= {1 \over 2 }(x)+1$

4. order

Yes

5. NotSObright

I think i solved it

6. shivam_bhalla

OK. Just put instead of cosec x , 1/2(x) +1

7. shivam_bhalla

Ok @NotSObright , let's see what you have done :P

8. NotSObright

Say y1=1/2x+1 y2=csc(x) y1(0)=1 y1(Pi/2)=Pi/4+1 y2(0)=infinty y2(Pi/2)=1 Since it can be proven using differentiation y1 is inceasing and y2 is decreasing on 0,pi/2 hence in order to attain boundary values graphs must cross each other

9. order

So what about the 0.5 and 1?

10. NotSObright

sorry i didn't see that u must show at 0.5 y1<y2 and at 1 y1>y2 u might wanna use a calculator

11. order

But how?

12. NotSObright

|dw:1336990897568:dw|

13. order

in calculation?

14. NotSObright

it is in calculation u need to calculate values at o.5 and 1 to show the inequality

15. order

So, how exactly?

16. NotSObright

i have told everything u need go through the conversation and try to use ur intelligence

17. order

hmm. ok..