# Find solution of eqation 2cot^2x-5cosec x =1

1. Mar 25, 2012

### vkash

2cot2(x)-5cosec(x)=1 for exactly 6 values of x belongs to [0,nπ], then find the minimum value of n.
How i did it.changing cot to cosec and then solving equation it will give something like cosec(x)=3. for x belongs to 0 to 5π it has 6 solutions..
this is question of a class test & answer in test's answer sheet is 6.
WHO IS correct. me or answer sheet???????

2. Mar 25, 2012

### rock.freak667

In 2π, you'd get 2 solutions A and 180-A. So for the next 2π, you'd have 4 in total and then in 2π again, you'd get 6.

So your range would be 6π.

3. Mar 25, 2012

### vkash

If i have got A and 180-A then i have got solutions in [0,π] not [0,2π] and in next 2π(or in [0,3π]) i will have 4 solution why i should go for 4π. similarly for next 5π.

Last edited: Mar 25, 2012
4. Mar 25, 2012

### SammyS

Staff Emeritus
You are correct for the problem that was given.

There are two roots in [0, π] ,

two roots in [2π, 3π] ,

and two roots in [4π, 5π] .

5. Mar 25, 2012

### vkash

thanks sammy..